Algebra 1 Unit 6B Factoring

Size: px
Start display at page:

Download "Algebra 1 Unit 6B Factoring"

Transcription

1 Algebra 1 Unit 6B Factoring Monday Tuesday Wednesday Thursday Friday 9 A Day 10 B Day 11 A Day 12 B Day 13 A Day Test Exponents and Polynomials Factor GCF and Trinomials box method Factoring Trinomials Feb B Day 18 A Day 19 B Day 20 A Day No School Staff Development Factoring Trinomials Factoring with Patterns GCF difference of squares perfect square trinomials Dividing Polynomials Retest CBA #4 Quiz Factoring 23 B Day 24 A Day 25 B Day 26 A Day 27 B Day Divide Polynomials Quiz Factoring Elaboration day Test CBA #6 (grade will need to go on the NEXT six weeks marking period) 1

2 WARM-UP # Simplify each expression. 1. (x + 4)(x 6) 2. (10x 2 + 5x 6) (8x 2 2x + 7) 3. 5x 2 (2xy 3x) 4. (2x + 5)(3x + 6) 5. (x 2 + y 2 ) (-x 2 + y 2 ) 6. a b ab

3 Notes GCF and Factoring Prime Number a whole number, greater than 1, whose only factors are 1 and itself Composite Number a whole number, greater than 1, that is not prime Prime Factorization a whole number expressed as a product of factors are all prime numbers (i.e. factor tree) Greatest Common Factor (GCF) the greatest common factor of two or more integers is the greatest number that is a factor of all the integers EX1: State whether each number is prime or composite. If the number if composite, find its prime factorization (tree). a. 28 b. 61 c. 112 d. 150 EX2: Find the GCF between two numbers using the calculator. a. -45, 15 b. 169, 13 c. -20, 440 d. 96, 12, -8 Greatest common factor for the same variable will be LOWEST exponent of that given variable. Factoring to express a polynomial as the product of a monomial and a polynomial EX3: Find the GCF for each set of monomials. a. x 2, x 5, x 4 b. 49x, 343x 2 c. 4a 7 b, 28ab d. 96y, 12x, -8y 3

4 EX4: Factor each polynomial. Notes GCF and Factoring a. 24w + 72z b. 30ab 2 + a 2 b 12ac 3 c. x 4 18x x d. a + 10a 2 b 3 e. 88x 4 11x x 5 f. 14c 3 42c 5 49c 4 g. 48w 2 x + 18wx 2 36wx h. -x 5 4x x 3 x 6 i. 8x 7y + w j. 18y 2 50 k. x 3 + 2x 2 + x 4

5 Reverse Distribution Find a monomial and a trinomial whose product is equal to each problem below. Cut and paste it in the correct place. Problems Monomials (GCF) Trinomials 1. 12x 2 + 3x x 4 6x 2 + 3x 3. 24x x 4 4x x 4 12x 3 + 6x x 3 24x 2 12x 6. 10a 4 b 2 5a 3 b + a 2 b 7. 5a 6 b a 5 b 4 15a 4 b a 5 b a 4 b 4 30a 3 b a 6 b 2 30a 5 b a 4 b a 7 b 6 15a 5 b a 3 5

6 Monomials (GCF) Trinomials 6x (10a 2 b 5a + 1) 5a 4 b 3 (10a 4 b 6 3a 2 b 2 + 5) 10a 4 b 2 (a 2 b 2 + 2ab 3) 5a 3 (4x 2 + x 2) 3 (x 2 4x 2) 3x (2x 2 6x + 3) a 2 b (2a 2 b 2 + ab 3) 10a 3 b 3 (6x 2 + 3x 1) 4x 3 (5a 2 3ab + b 2 ) 2x 2 (4x 3 2x + 1) 6

7 Name Date GCF and Factoring Factor out the GCF. 1. x 3 + x 2 + x 2. 15a + 12b + 6c 3. 8x 2 18y 2 4. x 2 y 2y 5. z 3 + 4z 6. 4x 2 4x 7. 15x 2 50x a 11b 9. 64c 3 56c c x 6 y 3 32x 3 y 2 20x 2 y x x x 3 y 4 40xy 5 7

8 Simplify each expression. 13. (2x + 5xy + 7y) + (3x + 7xy + y) 14. (3x + 2y) (5x + 6y) 40a b 15. (a + b) a b (2m -4 n 3 )(-5mn -7 ) 18. a b Find the volume of a cylinder with a diameter of 4x 3 y and a height of 7x 2 y Find the volume of a cube with sides 2b 3 r 2. Solve x + 2 = 2(5x 11) x < 10 8

9 WARM-UP # Find the missing information on the given rectangles What is the area? This is the same size rectangle just divided up What is the area of the first rectangle? 12 What is the area of the second rectangle? What is the area of the whole rectangle? Write the area of each rectangle inside each box for both of the rectangle below and answer the questions What is the total area of the rectangle? What is the total area of the rectangle? 6 What do you notice about all of the rectangles above? What is special about the length and width? What is the length and width of all the rectangles? 9

10 EXPLORE Given the rectangles below, determine the length and width of each rectangle and the area. Rectangles are not drawn to scale Total Area Total Area 6 Length Width 21 Length Width Total Area Length 2x 5x Total Area Length 21 Width Width 3x 2 2x Total Area Length 4x 2x 1 Total Area Length 30x 20 Width -1 Width x 2 Total Area Length x x 2-4 Total Area Length 30x 20 Width -12 Width Total Area Length (x 1) Width (2x + 3) 10

11 Notes Factoring Trinomials EX1. Recall the box method to multiply two binomials. Multiply (x 3)(x + 2). Factors: Product: EX2. Find the missing dimension of each trinomial s box. Fill in the blank cells in each box. a. a 2 + 7a + 10 = (a + 5)( ) b. c 2 10c + 21 = (c 3)( ) a a 2 c 2 c c. y 2 2y 15 = (y + 3) ( ) d. n 2 + 3n 28 = (n 4) ( ) y y 2 n 2 n e. How do the quantities you filled in the 2 blank cells relate to the original trinomial? 11

12 Notes Factoring Trinomials EX3. Write the numbers that give a sum of 5x and a product of 50x 2. Standard form: EX4. Factor each trinomial. a. x 2 + 7x + 10 = Sums to be: (Middle term: b) Yield a product of: (this comes from multiplying the a and c) b. x 2 + 3x 4 = Sums to be: (Middle term: b) Yield a product of: (this comes from multiplying the a and c) c. x 2 64 = Sums to be: (Middle term: b) Yield a product of: (this comes from multiplying the a and c) 12

13 Notes Factoring Trinomials d. 3x x + 8 = Sums to be: (Middle term: b) Yield a product of: (this comes from multiplying the a and c) e. 2y 2 7y + 6 = Sums to be: (Middle term: b) Yield a product of: (this comes from multiplying the a and c) f. 6x 2 21x 12 = Sums to be: (Middle term: b) Yield a product of: (this comes from multiplying the a and c) 13

14 Notes Factoring Trinomials Factoring Using Algebra Tiles EX5. Determine the factors of each polynomial. a. b. c. d. 14

15 Name Date A B C D E (x 2)(5x 8) (2x + 3)(3x 2) (x 13)(x + 3) (x + 2)(x 3) (x 2)(x + 3) F G H I J (x 8)(2x + 5) (x + 2)(7x + 3) (x 2)(x + 1) (x 5)(x + 3) (x + 5)(x 3) K L M N O (x 7)(x + 7) (x 2)(x 8) (x + 2)(x + 8) (x 7)(x 2) (x + 7) 2 P Q R S T (x 7)(x + 2) (x + 2)(x 8) (x 3)(x + 3) (x 6 )(2x 1) (x + 6) 2 U V W X Y (x 5)(x + 5) (x 5)(x 5) (x 3) 2 (x 3)(x + 20) (x 6)(x 2) Z (x + 9)(x + 7) Factoring Trinomials Directions: Match that answer to the correct letter of the alphabet. Enter that letter of the alphabet on the blank corresponding to the problem number. Factor each polynomial make sure to show your work. 1. x x x x x x 2 9x x 2 18x x 2 2x 15 15

16 7. x x 2 8x x 2 13x x 2 + x x 2 10x x 2 11x x x x 2 + 5x x 2 x x x x 2 9 Identify the simplified area of each rectangle. Then determine the factors

17 WARM-UP # 1. Factor: x x + 12 Factors: What did you notice? 2. Factor: 4x 2 9 Factors: What did you notice? 3. Factor: x 2 + 6x + 9 Factors: What did you notice? 17

18 18

19 Explain Factoring with Patterns Difference of Squares a 2 b 2 = (a) 2 (b) 2 = (a + b)(a b) difference opposite signs Conjugate pairs *Warning: a 2 + b 2 does not factor To recognize perfect squares, look for coefficients that are squares of integers and variables raised to even powers. EX1: Factor, if possible, using the difference of squares. a. 4x 2 9y 2 b. a 2 16b 2 c. 9x 4 25y 4 d. u 2 v 2 w 2 z 2 e. 25m n 2 19

20 Explain Factoring with Patterns Perfect Square Trinomials a 2 + 2ab + b 2 = (a + b)(a + b) = (a + b) 2 a 2 2ab + b 2 = (a b)(a b) = (a b) 2 EX2: Factor each of the following. a. x 2 + 6x + 9 b. x 2 10x + 25 c. a 2 + 8a + 16 d. 9a 2 24a

21 Name Date Factoring Patterns Determine whether each statement is TRUE. If not, find the correct product. 1. (3x + 1) 2 = 9x 2 + 6x (m 4) 2 = m 2 16m (5t 2) 2 = 25t 2 20t (2n + 7) 2 = 4n n (2b + 3) 2 = 4b b (2a + b) 2 = 4a 2 + 4ab + b 2 Factor each polynomial. If it cannot be factored, write prime. 7. t 2 12t a 2 + 2ab + b t t n n a 2 24ab + 9b 2 21

22 13. t 2 18t n t + t n m 2 16n a 2 8a a a n Which is the correct factorization of 45x y 2? A. 5(3x + 2y) 2 B. 5(3x 2y) 2 C. 5(3x + 2y)(3x 2y) D. 5(3x + 2y)(3x 2y) 22. Challenge Determine the value(s) of k for which each expression is a perfect square trinomial. a. 49x 2 84k + k b. 4x 2 + kx

23 Explore Dividing Polynomials Remember when we MULTIPLIED: (using a box) (x + 2)(x + 6) or (2y + 1)(3y 4) So can you now DIVIDE these polynomials: (using a box) x 2 + 8x + 12 x + 2 6y 2 5y 4 3y 4 3y 4 x +2 So.. x 2 + 8x + 12 x + 2 the quotient is: 6y 2 5y 4 3y 4 the quotient is: 23

24 24

25 Explain Dividing Polynomials Dividing is the opposite operation of. Therefore, we will use the to assist in dividing trinomials when given a trinomial divided by a binomial. EX1. Simplify each expression. a. x 2 + 4x 5 x 1 Quotient: x x 2 5x 1 x 5 b. 2x x + 12 x + 4 Quotient: 2x 2 8x 3x 12 c. 6x x 5 3x 1 Quotient: 25

26 Explain Dividing Polynomials EX2. Simplify each expression ON OUR OWN. a. 5x x 14 x + 7 Quotient: b. x 2 11x + 24 x 8 Quotient: c. 2x x 9 2x 1 Quotient: 26

27 Name Gingerbread Man Date Divide each polynomial. Each answer determines the next location of the traveling gingerbread man. Determine the path the gingerbread man makes through the school. 1. x x + 27 x x 2 13x + 40 x 8 3. x 2 7x 44 x x 2 + x 42 x x 2 + 9x + 4 2x x 2 15x + 7 x x 2 + 7x 15 2x x x + 5 2x x x 14 x x 2 + 7x 12 3x x 2 + 2x 3 2x x 2 15x + 4 3x 4 27

28 Front Door Cafeteria (3x 1) Principal Counselor Nurse (x 2) (4x + 3) (x + 11) Secretary (4x 3) Attendance (x + 1) Trophy case (3x 2) Teacher Workroom K - 2 Kindergarte n 1 st Grade 2 nd Grade (x + 2) (2x 1) (3x + 1) Library 3 rd Grade (x 4) (x + 5) Playground 2 (x + 6) (x 5) 4 th Grade 5 th Grade (3x + 2) (x + 4) Teacher Workroom 3 5 Theater (x + 3) Home Ec Lab Where s my class? Computer Lab (x 11) Art Room (x + 7) Playground 1 (x 7) 28

29 Name Date 1. Find the volume of a cube with sides 2b 3 r 2. Review CBA #6 2. Find the volume of a cylinder that has a radius of 5s 3 t 5 and a height of 2s 2 t Find the area of a triangle that has a base of 32mn 7 and a height of 3m 4 n If a rectangle has an area of 16x 7 y 4 and a length of 4x 3 y, what is its width? 5. Distance (d), rate (r), and time (t) are related by the formula d = rt. If a ball rolls 36p 4 q 9 feet for 4p 2 q 3 minutes, what is the rate? 6. Write an expression that best represents the area of a square with sides of 7x 4 y 3? 7. Find the perimeter and area of the rectangle in terms of n. 3n 5 2n

30 8. Find the perimeter and area of the triangle in terms of x. 3n + 5 5n 1 2n Simplify each expression. 9. (-2x + x 2 ) x(5x 4) + (9x 2 6x) 10. p(2p 3) + (p 3)(4p + 1) 11. (3x 5 ) 3 (2x 7 ) (-3x 6 ) (3r + 7) x y z x y z ( 2a b ) ( 7ab ) a b n 6 + n + n The dimensions of a wall are 7xy feet by 8x 2 y 3 feet. A picture has dimensions 2x feet by x 2 y 4 feet. If the picture is hanging on the wall as shown, what is the area of the wall not covered by the picture? 18. A pitcher contains 16x 5 y 4 ounces of water. A mug holds 2x 2 y ounces. Leticia pours water from the full pitcher into mugs. If she filled ax b y c mugs, what is the value of a + b + c? 30

31 19. Find the area of a circle with radius 6r 3 s 5 inches. 20. Find the area of a rectangle with side lengths (x 2 7x) and (2x 2 + 3x + 1). 21. Describe and correct the error in finding the product of the given polynomials. 22. The area of a rectangle is 3x 2 10x 8. Find the dimensions (length and width) of the rectangle. Factor out the greatest common monomial factor a 2 40b s s 2 54s abc 2 6a 2 c 31

32 Completely factor each of the following polynomials. 26. r 2 + 2r y 2 2y x x ax 2 3ax 35a 30. 4a 2 + 9a k k x k u 2 25 Identify the simplified area of each rectangle. Then determine the factors

Chapter 5: Exponents and Polynomials

Chapter 5: Exponents and Polynomials Chapter 5: Exponents and Polynomials 5.1 Multiplication with Exponents and Scientific Notation 5.2 Division with Exponents 5.3 Operations with Monomials 5.4 Addition and Subtraction of Polynomials 5.5

More information

Algebra I. Exponents and Polynomials. Name

Algebra I. Exponents and Polynomials. Name Algebra I Exponents and Polynomials Name 1 2 UNIT SELF-TEST QUESTIONS The Unit Organizer #6 2 LAST UNIT /Experience NAME 4 BIGGER PICTURE DATE Operations with Numbers and Variables 1 CURRENT CURRENT UNIT

More information

Algebra I. Polynomials.

Algebra I. Polynomials. 1 Algebra I Polynomials 2015 11 02 www.njctl.org 2 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying a Polynomial by a Monomial Multiplying

More information

Algebra I Polynomials

Algebra I Polynomials Slide 1 / 217 Slide 2 / 217 Algebra I Polynomials 2014-04-24 www.njctl.org Slide 3 / 217 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying

More information

Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers

Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Chapter 3: Section 3.1: Factors & Multiples of Whole Numbers Prime Factor: a prime number that is a factor of a number. The first 15 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,

More information

Multiplication of Polynomials

Multiplication of Polynomials Summary 391 Chapter 5 SUMMARY Section 5.1 A polynomial in x is defined by a finite sum of terms of the form ax n, where a is a real number and n is a whole number. a is the coefficient of the term. n is

More information

Collecting Like Terms

Collecting Like Terms MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.

More information

LESSON 9.1 ROOTS AND RADICALS

LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical

More information

Secondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics

Secondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics Secondary Math H Unit 3 Notes: Factoring and Solving Quadratics 3.1 Factoring out the Greatest Common Factor (GCF) Factoring: The reverse of multiplying. It means figuring out what you would multiply together

More information

Math 10-C Polynomials Concept Sheets

Math 10-C Polynomials Concept Sheets Math 10-C Polynomials Concept Sheets Concept 1: Polynomial Intro & Review A polynomial is a mathematical expression with one or more terms in which the exponents are whole numbers and the coefficients

More information

Assignment #1 MAT121 Summer 2015 NAME:

Assignment #1 MAT121 Summer 2015 NAME: Assignment #1 MAT11 Summer 015 NAME: Directions: Do ALL of your work on THIS handout in the space provided! Circle your final answer! On problems that your teacher would show work on be sure that you also

More information

UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name:

UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name: UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay

More information

Ready To Go On? Skills Intervention 7-1 Integer Exponents

Ready To Go On? Skills Intervention 7-1 Integer Exponents 7A Evaluating Expressions with Zero and Negative Exponents Zero Exponent: Any nonzero number raised to the zero power is. 4 0 Ready To Go On? Skills Intervention 7-1 Integer Exponents Negative Exponent:

More information

Never leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!!

Never leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!! 1 ICM Unit 0 Algebra Rules Lesson 1 Rules of Exponents RULE EXAMPLE EXPLANANTION a m a n = a m+n A) x x 6 = B) x 4 y 8 x 3 yz = When multiplying with like bases, keep the base and add the exponents. a

More information

Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10. Unit 8. [Polynomials] Unit 8 Polynomials 1

Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10. Unit 8. [Polynomials] Unit 8 Polynomials 1 Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 8 [Polynomials] Unit 8 Polynomials 1 To be a Successful Algebra class, TIGERs will show #TENACITY during

More information

Unit 3 Factors & Products

Unit 3 Factors & Products 1 Unit 3 Factors & Products General Outcome: Develop algebraic reasoning and number sense. Specific Outcomes: 3.1 Demonstrate an understanding of factors of whole number by determining the: o prime factors

More information

MATHEMATICS 9 CHAPTER 7 MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT NAME: DATE: BLOCK: TEACHER: Miller High School Mathematics Page 1

MATHEMATICS 9 CHAPTER 7 MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT NAME: DATE: BLOCK: TEACHER: Miller High School Mathematics Page 1 MATHEMATICS 9 CHAPTER 7 NAME: DATE: BLOCK: TEACHER: MILLER HIGH SCHOOL MATHEMATICS DEPARTMENT Miller High School Mathematics Page 1 Day 1: Creating expressions with algebra tiles 1. Determine the multiplication

More information

MATH98 Intermediate Algebra Practice Test Form A

MATH98 Intermediate Algebra Practice Test Form A MATH98 Intermediate Algebra Practice Test Form A MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y - 4) - (y + ) = 3y 1) A)

More information

Mathwithsheppard.weebly.com

Mathwithsheppard.weebly.com Unit #: Powers and Polynomials Unit Outline: Date Lesson Title Assignment Completed.1 Introduction to Algebra. Discovering the Exponent Laws Part 1. Discovering the Exponent Laws Part. Multiplying and

More information

Algebra 2. Factoring Polynomials

Algebra 2. Factoring Polynomials Algebra 2 Factoring Polynomials Algebra 2 Bell Ringer Martin-Gay, Developmental Mathematics 2 Algebra 2 Bell Ringer Answer: A Martin-Gay, Developmental Mathematics 3 Daily Learning Target (DLT) Tuesday

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t 4 3. 8s 4 + 4s 6 5s 4. 9m + 3 + m 3 + 5m 5. 4 3p 7 3p 4 1 z 1 + 4 6. ( ) 7. 6( x + ) 4 8. 3( h + 4) 3( h

More information

Solving Multi-Step Equations

Solving Multi-Step Equations 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract terms to both sides of the equation to get the

More information

Unit 3A: Factoring & Solving Quadratic Equations After completion of this unit, you will be able to

Unit 3A: Factoring & Solving Quadratic Equations After completion of this unit, you will be able to Unit 3A: Factoring & Solving Quadratic Equations After completion of this unit, you will be able to Learning Target #1: Factoring Factor the GCF out of a polynomial Factor a polynomial when a = 1 Factor

More information

POLYNOMIAL: A polynomial is a or the

POLYNOMIAL: A polynomial is a or the MONOMIALS: CC Math I Standards: Unit 6 POLYNOMIALS: INTRODUCTION EXAMPLES: A number 4 y a 1 x y A variable NON-EXAMPLES: Variable as an exponent A sum x x 3 The product of variables 5a The product of numbers

More information

Unit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions

Unit 2-1: Factoring and Solving Quadratics. 0. I can add, subtract and multiply polynomial expressions CP Algebra Unit -1: Factoring and Solving Quadratics NOTE PACKET Name: Period Learning Targets: 0. I can add, subtract and multiply polynomial expressions 1. I can factor using GCF.. I can factor by grouping.

More information

Algebra I Unit Report Summary

Algebra I Unit Report Summary Algebra I Unit Report Summary No. Objective Code NCTM Standards Objective Title Real Numbers and Variables Unit - ( Ascend Default unit) 1. A01_01_01 H-A-B.1 Word Phrases As Algebraic Expressions 2. A01_01_02

More information

Review for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition.

Review for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition. LESSON 6- Review for Mastery Integer Exponents Remember that means 8. The base is, the exponent is positive. Exponents can also be 0 or negative. Zero Exponents Negative Exponents Negative Exponents in

More information

Algebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals

Algebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive

More information

Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together.

Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together. UNIT 10 Working with Polynomials The railcars are linked together. 370 UNIT 10 WORKING WITH POLYNOMIALS Just as a train is built from linking railcars together, a polynomial is built by bringing terms

More information

Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions.

Something that can have different values at different times. A variable is usually represented by a letter in algebraic expressions. Lesson Objectives: Students will be able to define, recognize and use the following terms in the context of polynomials: o Constant o Variable o Monomial o Binomial o Trinomial o Polynomial o Numerical

More information

P.1: Algebraic Expressions, Mathematical Models, and Real Numbers

P.1: Algebraic Expressions, Mathematical Models, and Real Numbers Chapter P Prerequisites: Fundamental Concepts of Algebra Pre-calculus notes Date: P.1: Algebraic Expressions, Mathematical Models, and Real Numbers Algebraic expression: a combination of variables and

More information

27 Wyner Math 2 Spring 2019

27 Wyner Math 2 Spring 2019 27 Wyner Math 2 Spring 2019 CHAPTER SIX: POLYNOMIALS Review January 25 Test February 8 Thorough understanding and fluency of the concepts and methods in this chapter is a cornerstone to success in the

More information

MathB65 Ch 4 IV, V, VI.notebook. October 31, 2017

MathB65 Ch 4 IV, V, VI.notebook. October 31, 2017 Part 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest

More information

Algebra I. Slide 1 / 216. Slide 2 / 216. Slide 3 / 216. Polynomials

Algebra I. Slide 1 / 216. Slide 2 / 216. Slide 3 / 216. Polynomials Slide 1 / 216 Slide 2 / 216 lgebra I Polynomials 2015-11-02 www.njctl.org Table of ontents efinitions of Monomials, Polynomials and egrees dding and Subtracting Polynomials Multiplying a Polynomial by

More information

mn 3 17x 2 81y 4 z Algebra I Definitions of Monomials, Polynomials and Degrees 32,457 Slide 1 / 216 Slide 2 / 216 Slide 3 / 216 Slide 4 / 216

mn 3 17x 2 81y 4 z Algebra I Definitions of Monomials, Polynomials and Degrees 32,457 Slide 1 / 216 Slide 2 / 216 Slide 3 / 216 Slide 4 / 216 Slide 1 / 216 Slide 2 / 216 lgebra I Polynomials 2015-11-02 www.njctl.org Slide 3 / 216 Table of ontents efinitions of Monomials, Polynomials and egrees dding and Subtracting Polynomials Multiplying a

More information

Algebra 1 Unit 6 Notes

Algebra 1 Unit 6 Notes Algebra 1 Unit 6 Notes Name: Day Date Assignment (Due the next class meeting) Monday Tuesday Wednesday Thursday Friday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday

More information

5.3. Polynomials and Polynomial Functions

5.3. Polynomials and Polynomial Functions 5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a

More information

Classifying Polynomials. Simplifying Polynomials

Classifying Polynomials. Simplifying Polynomials 1 Classifying Polynomials A polynomial is an algebraic expression with one or more unlike terms linked together by + or **Polynomials can be classified by the number of terms they have: A monomial has

More information

When factoring, we ALWAYS start with the (unless it s 1).

When factoring, we ALWAYS start with the (unless it s 1). Math 100 Elementary Algebra Sec 5.1: The Greatest Common Factor and Factor By Grouping (FBG) Recall: In the product XY, X and Y are factors. Defn In an expression, any factor that is common to each term

More information

ACTIVITY: Factoring Special Products. Work with a partner. Six different algebra tiles are shown below.

ACTIVITY: Factoring Special Products. Work with a partner. Six different algebra tiles are shown below. 7.9 Factoring Special Products special products? How can you recognize and factor 1 ACTIVITY: Factoring Special Products Work with a partner. Six different algebra tiles are shown below. 1 1 x x x 2 x

More information

When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut.

When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut. Squaring a Binomial When you square a binomial, you can apply the FOIL method to find the product. You can also apply the following rules as a short cut. Solve. (x 3) 2 Step 1 Square the first term. Rules

More information

Bishop Kelley High School Summer Math Program Course: Algebra 2 A

Bishop Kelley High School Summer Math Program Course: Algebra 2 A 06 07 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 6 pages of this packet provide eamples as to how to work some of the problems

More information

Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2

Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 April 11, 2016 Chapter 10 Section 1: Addition and Subtraction of Polynomials A monomial is

More information

Review Unit Multiple Choice Identify the choice that best completes the statement or answers the question.

Review Unit Multiple Choice Identify the choice that best completes the statement or answers the question. Review Unit 3 1201 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following numbers is not both a perfect square and a perfect cube? a. 531

More information

CHAPTER 1 POLYNOMIALS

CHAPTER 1 POLYNOMIALS 1 CHAPTER 1 POLYNOMIALS 1.1 Removing Nested Symbols of Grouping Simplify. 1. 4x + 3( x ) + 4( x + 1). ( ) 3x + 4 5 x 3 + x 3. 3 5( y 4) + 6 y ( y + 3) 4. 3 n ( n + 5) 4 ( n + 8) 5. ( x + 5) x + 3( x 6)

More information

Rising 8th Grade Math. Algebra 1 Summer Review Packet

Rising 8th Grade Math. Algebra 1 Summer Review Packet Rising 8th Grade Math Algebra 1 Summer Review Packet 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract

More information

Polynomials. This booklet belongs to: Period

Polynomials. This booklet belongs to: Period HW Mark: 10 9 8 7 6 RE-Submit Polynomials This booklet belongs to: Period LESSON # DATE QUESTIONS FROM NOTES Questions that I find difficult Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. Pg. REVIEW TEST Your teacher

More information

Unit 13: Polynomials and Exponents

Unit 13: Polynomials and Exponents Section 13.1: Polynomials Section 13.2: Operations on Polynomials Section 13.3: Properties of Exponents Section 13.4: Multiplication of Polynomials Section 13.5: Applications from Geometry Section 13.6:

More information

Topic 7: Polynomials. Introduction to Polynomials. Table of Contents. Vocab. Degree of a Polynomial. Vocab. A. 11x 7 + 3x 3

Topic 7: Polynomials. Introduction to Polynomials. Table of Contents. Vocab. Degree of a Polynomial. Vocab. A. 11x 7 + 3x 3 Topic 7: Polynomials Table of Contents 1. Introduction to Polynomials. Adding & Subtracting Polynomials 3. Multiplying Polynomials 4. Special Products of Binomials 5. Factoring Polynomials 6. Factoring

More information

Lesson 3: Polynomials and Exponents, Part 1

Lesson 3: Polynomials and Exponents, Part 1 Lesson 2: Introduction to Variables Assessment Lesson 3: Polynomials and Exponents, Part 1 When working with algebraic expressions, variables raised to a power play a major role. In this lesson, we look

More information

LESSON 7.2 FACTORING POLYNOMIALS II

LESSON 7.2 FACTORING POLYNOMIALS II LESSON 7.2 FACTORING POLYNOMIALS II LESSON 7.2 FACTORING POLYNOMIALS II 305 OVERVIEW Here s what you ll learn in this lesson: Trinomials I a. Factoring trinomials of the form x 2 + bx + c; x 2 + bxy +

More information

PRE-ALGEBRA SUMMARY WHOLE NUMBERS

PRE-ALGEBRA SUMMARY WHOLE NUMBERS PRE-ALGEBRA SUMMARY WHOLE NUMBERS Introduction to Whole Numbers and Place Value Digits Digits are the basic symbols of the system 0,,,, 4,, 6, 7, 8, and 9 are digits Place Value The value of a digit in

More information

LESSON 6.2 POLYNOMIAL OPERATIONS I

LESSON 6.2 POLYNOMIAL OPERATIONS I LESSON 6.2 POLYNOMIAL OPERATIONS I Overview In business, people use algebra everyday to find unknown quantities. For example, a manufacturer may use algebra to determine a product s selling price in order

More information

Math 46 Final Exam Review Packet

Math 46 Final Exam Review Packet Math 46 Final Exam Review Packet Question 1. Perform the indicated operation. Simplify if possible. 7 x x 2 2x + 3 2 x Question 2. The sum of a number and its square is 72. Find the number. Question 3.

More information

Chapter Six. Polynomials. Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring

Chapter Six. Polynomials. Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring Chapter Six Polynomials Properties of Exponents Algebraic Expressions Addition, Subtraction, and Multiplication Factoring Solving by Factoring Properties of Exponents The properties below form the basis

More information

Big Bend Community College. Beginning Algebra MPC 095. Lab Notebook

Big Bend Community College. Beginning Algebra MPC 095. Lab Notebook Big Bend Community College Beginning Algebra MPC 095 Lab Notebook Beginning Algebra Lab Notebook by Tyler Wallace is licensed under a Creative Commons Attribution 3.0 Unported License. Permissions beyond

More information

Example #3: 14 (5 + 2) 6 = = then add = 1 x (-3) then. = 1.5 = add

Example #3: 14 (5 + 2) 6 = = then add = 1 x (-3) then. = 1.5 = add Grade 9 Curricular content Operations with rational numbers (addition, subtraction, multiplication, division and order of operations) -incudes brackets and exponents (exponent laws) -exponents includes

More information

9-1 Skills Practice Factors and Greatest Common Factors Find the factors of each number. Then classify each number as prime or composite

9-1 Skills Practice Factors and Greatest Common Factors Find the factors of each number. Then classify each number as prime or composite 9-1 Skills Practice Factors and Greatest Common Factors Find the factors of each number. Then classify each number as prime or composite. 1. 10 2. 31 3. 16 4. 52 5. 38 6. 105 Find the prime factorization

More information

The number part of a term with a variable part. Terms that have the same variable parts. Constant terms are also like terms.

The number part of a term with a variable part. Terms that have the same variable parts. Constant terms are also like terms. Algebra Notes Section 9.1: Add and Subtract Polynomials Objective(s): To be able to add and subtract polynomials. Recall: Coefficient (p. 97): Term of a polynomial (p. 97): Like Terms (p. 97): The number

More information

Quadratic Expressions and Equations

Quadratic Expressions and Equations Unit 5 Quadratic Expressions and Equations 1/9/2017 2/8/2017 Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials

More information

My Math Plan Assessment #1 Study Guide

My Math Plan Assessment #1 Study Guide My Math Plan Assessment #1 Study Guide 1. Find the x-intercept and the y-intercept of the linear equation. 8x y = 4. Use factoring to solve the quadratic equation. x + 9x + 1 = 17. Find the difference.

More information

Adding and Subtracting Polynomials

Adding and Subtracting Polynomials Adding and Subtracting Polynomials Polynomial A monomial or sum of monomials. Binomials and Trinomial are also polynomials. Binomials are sum of two monomials Trinomials are sum of three monomials Degree

More information

8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors

8-1 Factors and Greatest Common Factors 8-1. Factors and Greatest Common Factors 8-1 Factors and Greatest Common Factors Warm Up Lesson Presentation Lesson Quiz 1 2 pts 2 pts Bell Quiz 8-1 Tell whether the second number is a factor of the first number 1. 50, 6 2 pts no 2. 105, 7 3.

More information

7.7. Factoring Special Products. Essential Question How can you recognize and factor special products?

7.7. Factoring Special Products. Essential Question How can you recognize and factor special products? 7.7 Factoring Special Products Essential Question How can you recognize and factor special products? Factoring Special Products LOOKING FOR STRUCTURE To be proficient in math, you need to see complicated

More information

Algebra 1: Hutschenreuter Chapter 10 Notes Adding and Subtracting Polynomials

Algebra 1: Hutschenreuter Chapter 10 Notes Adding and Subtracting Polynomials Algebra 1: Hutschenreuter Chapter 10 Notes Name 10.1 Adding and Subtracting Polynomials Polynomial- an expression where terms are being either added and/or subtracted together Ex: 6x 4 + 3x 3 + 5x 2 +

More information

Beginning Algebra MAT0024C. Professor Sikora. Professor M. J. Sikora ~ Valencia Community College

Beginning Algebra MAT0024C. Professor Sikora. Professor M. J. Sikora ~ Valencia Community College Beginning Algebra Professor Sikora MAT002C POLYNOMIALS 6.1 Positive Integer Exponents x n = x x x x x [n of these x factors] base exponent Numerical: Ex: - = where as Ex: (-) = Ex: - = and Ex: (-) = Rule:

More information

Remember, you may not use a calculator when you take the assessment test.

Remember, you may not use a calculator when you take the assessment test. Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation.

More information

Prime Factorization and GCF. In my own words

Prime Factorization and GCF. In my own words Warm- up Problem What is a prime number? A PRIME number is an INTEGER greater than 1 with EXACTLY 2 positive factors, 1 and the number ITSELF. Examples of prime numbers: 2, 3, 5, 7 What is a composite

More information

Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x ) A) x = 5 B) x = -6 C) x = -5 D) x = 6

Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x ) A) x = 5 B) x = -6 C) x = -5 D) x = 6 Review for Final Exam Math 124A (Flatley) Name Which one of the following is the solution to the equation? 1) 4(x - 2) + 6 = 2x - 14 1) A) x = 5 B) x = -6 C) x = -5 D) x = 6 Solve the linear equation.

More information

Chapter 8 Polynomials and Factoring

Chapter 8 Polynomials and Factoring Chapter 8 Polynomials and Factoring 8.1 Add and Subtract Polynomials Monomial A. EX: Degree of a monomial the of all of the of the EX: 4x 2 y Polynomial A or EX: Degree of a polynomial the of its terms

More information

Simplify each numerical expression. Show all work! Only use a calculator to check. 1) x ) 25 ( x 2 3) 3) 4)

Simplify each numerical expression. Show all work! Only use a calculator to check. 1) x ) 25 ( x 2 3) 3) 4) NAME HONORS ALGEBRA II REVIEW PACKET To maintain a high quality program, students entering Honors Algebra II are expected to remember the basics of the mathematics taught in their Algebra I course. In

More information

SECTION 1.4 PolyNomiAls feet. Figure 1. A = s 2 = (2x) 2 = 4x 2 A = 2 (2x) 3 _ 2 = 1 _ = 3 _. A = lw = x 1. = x

SECTION 1.4 PolyNomiAls feet. Figure 1. A = s 2 = (2x) 2 = 4x 2 A = 2 (2x) 3 _ 2 = 1 _ = 3 _. A = lw = x 1. = x SECTION 1.4 PolyNomiAls 4 1 learning ObjeCTIveS In this section, you will: Identify the degree and leading coefficient of polynomials. Add and subtract polynomials. Multiply polynomials. Use FOIL to multiply

More information

Lecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 3rd edition. Miller, O'Neill, & Hyde. Victor Valley College

Lecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 3rd edition. Miller, O'Neill, & Hyde. Victor Valley College Lecture Guide Math 90 - Intermediate Algebra to accompany Intermediate Algebra, 3rd edition Miller, O'Neill, & Hyde Prepared by Stephen Toner Victor Valley College Last updated: 4/17/16 5.1 Exponents &

More information

Properties of Real Numbers

Properties of Real Numbers Pre-Algebra Properties of Real Numbers Identity Properties Addition: Multiplication: Commutative Properties Addition: Multiplication: Associative Properties Inverse Properties Distributive Properties Properties

More information

Additional Exercises 7.1 Form I The Greatest Common Factor and Factoring by Grouping

Additional Exercises 7.1 Form I The Greatest Common Factor and Factoring by Grouping Additional Exercises 7.1 Form I The Greatest Common Factor and Factoring by Grouping Find the greatest common factor of each list of monomials. 1. 10x and 15 x 1.. 3 1y and 8y. 3. 16 a 3 a, 4 and 4 3a

More information

Grade 9 Mathematics Unit #2 Patterns & Relations Sub-Unit #1 Polynomials

Grade 9 Mathematics Unit #2 Patterns & Relations Sub-Unit #1 Polynomials Grade 9 Mathematics Unit #2 Patterns & Relations Sub-Unit #1 Polynomials Lesson Topic I Can 1 Definitions Define Polynomials Identify Polynomials Identify different parts of a polynomial Identify monomials,

More information

{ independent variable some property or restriction about independent variable } where the vertical line is read such that.

{ independent variable some property or restriction about independent variable } where the vertical line is read such that. Page 1 of 5 Introduction to Review Materials One key to Algebra success is identifying the type of work necessary to answer a specific question. First you need to identify whether you are dealing with

More information

LESSON 6.2 POLYNOMIAL OPERATIONS I

LESSON 6.2 POLYNOMIAL OPERATIONS I LESSON 6. POLYNOMIAL OPERATIONS I LESSON 6. POLYNOMIALS OPERATIONS I 63 OVERVIEW Here's what you'll learn in this lesson: Adding and Subtracting a. Definition of polynomial, term, and coefficient b. Evaluating

More information

1.3 Algebraic Expressions. Copyright Cengage Learning. All rights reserved.

1.3 Algebraic Expressions. Copyright Cengage Learning. All rights reserved. 1.3 Algebraic Expressions Copyright Cengage Learning. All rights reserved. Objectives Adding and Subtracting Polynomials Multiplying Algebraic Expressions Special Product Formulas Factoring Common Factors

More information

A-2. Polynomials and Factoring. Section A-2 1

A-2. Polynomials and Factoring. Section A-2 1 A- Polynomials and Factoring Section A- 1 What you ll learn about Adding, Subtracting, and Multiplying Polynomials Special Products Factoring Polynomials Using Special Products Factoring Trinomials Factoring

More information

We say that a polynomial is in the standard form if it is written in the order of decreasing exponents of x. Operations on polynomials:

We say that a polynomial is in the standard form if it is written in the order of decreasing exponents of x. Operations on polynomials: R.4 Polynomials in one variable A monomial: an algebraic expression of the form ax n, where a is a real number, x is a variable and n is a nonnegative integer. : x,, 7 A binomial is the sum (or difference)

More information

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives:

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives: Math 65 / Notes & Practice #1 / 20 points / Due. / Name: Home Work Practice: Simplify the following expressions by reducing the fractions: 16 = 4 = 8xy =? = 9 40 32 38x 64 16 Solve the following equations

More information

Review Notes - Solving Quadratic Equations

Review Notes - Solving Quadratic Equations Review Notes - Solving Quadratic Equations What does solve mean? Methods for Solving Quadratic Equations: Solving by using Square Roots Solving by Factoring using the Zero Product Property Solving by Quadratic

More information

Section 9.1: Add and Subtract Polynomials. The number part of a term with a variable part.

Section 9.1: Add and Subtract Polynomials. The number part of a term with a variable part. Algebra Notes Section 9.1: Add and Subtract Polynomials Objective(s): Recall: Coefficient (p. 97): Term of a polynomial (p. 97): Like Terms (p. 97): The number part of a term with a variable part. The

More information

Lesson 6. Diana Pell. Monday, March 17. Section 4.1: Solve Linear Inequalities Using Properties of Inequality

Lesson 6. Diana Pell. Monday, March 17. Section 4.1: Solve Linear Inequalities Using Properties of Inequality Lesson 6 Diana Pell Monday, March 17 Section 4.1: Solve Linear Inequalities Using Properties of Inequality Example 1. Solve each inequality. Graph the solution set and write it using interval notation.

More information

MathB65 Ch 4 VII, VIII, IX.notebook. November 06, 2017

MathB65 Ch 4 VII, VIII, IX.notebook. November 06, 2017 Chapter 4: Polynomials I. Exponents & Their Properties II. Negative Exponents III. Scientific Notation IV. Polynomials V. Addition & Subtraction of Polynomials VI. Multiplication of Polynomials VII. Greatest

More information

How to write polynomials in standard form How to add, subtract, and multiply polynomials How to use special products to multiply polynomials

How to write polynomials in standard form How to add, subtract, and multiply polynomials How to use special products to multiply polynomials PRC Ch P_3.notebook How to write polynomials in standard form How to add, subtract, and multiply polynomials How to use special products to multiply polynomials How to remove common factors from polynomials

More information

5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014. c = Properites of Exponents. *Simplify each of the following:

5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014. c = Properites of Exponents. *Simplify each of the following: 48 5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014 Properites of Exponents 1. x a x b = x a+b *Simplify each of the following: a. x 4 x 8 = b. x 5 x 7 x = 2. xa xb = xa b c. 5 6 5 11 = d. x14

More information

2009 Math Olympics Level II

2009 Math Olympics Level II Saginaw Valley State University 009 Math Olympics Level II 1. f x) is a degree three monic polynomial leading coefficient is 1) such that f 0) = 3, f 1) = 5 and f ) = 11. What is f 5)? a) 7 b) 113 c) 16

More information

8-1: Adding and Subtracting Polynomials

8-1: Adding and Subtracting Polynomials 8-1: Adding and Subtracting Polynomials Objective: To classify, add, and subtract polynomials Warm Up: Simplify each expression. 1. x 3 7 x 9. 6(3x 4) 3. 7 ( x 8) 4 4. 5(4x (8x 6) monomial - A real number,

More information

Section 6.5 A General Factoring Strategy

Section 6.5 A General Factoring Strategy Difference of Two Squares: a 2 b 2 = (a + b)(a b) NOTE: Sum of Two Squares, a 2 b 2, is not factorable Sum and Differences of Two Cubes: a 3 + b 3 = (a + b)(a 2 ab + b 2 ) a 3 b 3 = (a b)(a 2 + ab + b

More information

LESSON 6.3 POLYNOMIAL OPERATIONS II

LESSON 6.3 POLYNOMIAL OPERATIONS II LESSON 6.3 POLYNOMIAL OPERATIONS II LESSON 6.3 POLYNOMIALS OPERATIONS II 277 OVERVIEW Here's what you'll learn in this lesson: Multiplying Binomials a. Multiplying binomials by the FOIL method b. Perfect

More information

Quick-and-Easy Factoring. of lower degree; several processes are available to fi nd factors.

Quick-and-Easy Factoring. of lower degree; several processes are available to fi nd factors. Lesson 11-3 Quick-and-Easy Factoring BIG IDEA Some polynomials can be factored into polynomials of lower degree; several processes are available to fi nd factors. Vocabulary factoring a polynomial factored

More information

Unit 5 Quadratic Expressions and Equations

Unit 5 Quadratic Expressions and Equations Unit 5 Quadratic Expressions and Equations Test Date: Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials and

More information

Prerequisites. Copyright Cengage Learning. All rights reserved.

Prerequisites. Copyright Cengage Learning. All rights reserved. Prerequisites P Copyright Cengage Learning. All rights reserved. P.4 FACTORING POLYNOMIALS Copyright Cengage Learning. All rights reserved. What You Should Learn Remove common factors from polynomials.

More information

Math 0320 Final Exam Review

Math 0320 Final Exam Review Math 0320 Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Factor out the GCF using the Distributive Property. 1) 6x 3 + 9x 1) Objective:

More information

review To find the coefficient of all the terms in 15ab + 60bc 17ca: Coefficient of ab = 15 Coefficient of bc = 60 Coefficient of ca = -17

review To find the coefficient of all the terms in 15ab + 60bc 17ca: Coefficient of ab = 15 Coefficient of bc = 60 Coefficient of ca = -17 1. Revision Recall basic terms of algebraic expressions like Variable, Constant, Term, Coefficient, Polynomial etc. The coefficients of the terms in 4x 2 5xy + 6y 2 are Coefficient of 4x 2 is 4 Coefficient

More information

3 According to the standard convention for exponentiation,

3 According to the standard convention for exponentiation, AMC 10 2002 A 1 The ratio 102000 +10 2002 10 2001 is closest to which of the following numbers? +102001 (A) 0.1 (B) 0.2 (C) 1 (D) 5 (E) 10 2 For the nonzero numbers a, b, c, define (a,b,c) = a b + b c

More information

Combining Like Terms in Polynomials

Combining Like Terms in Polynomials Section 1 6: Combining Like Terms in Polynomials Polynomials A polynomial is an expression that has two or more terms each separated by a + or sign. If the expression has only one term it is called a monomial.

More information

Math 75 Mini-Mod Due Dates Spring 2016

Math 75 Mini-Mod Due Dates Spring 2016 Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing

More information