4.1 Practice A. Name Date. as x +. Describe the degree and leading coefficient of the function. as x and f( x)

Size: px
Start display at page:

Download "4.1 Practice A. Name Date. as x +. Describe the degree and leading coefficient of the function. as x and f( x)"

Transcription

1 Name Date. Practice A In Exercises, decide whether the function is a polnomial function. If so, write it in standard form and state its degree, tpe, and leading coefficient.. f( x) = x x + 5x 7. ( ). g( x) = x x + 0 x + x. ( ) In Exercises 5 7, evaluate the function for the given value of x. f x = x + x + 5x x 7; x = 5. ( ) gx = 5x x + 9x 0; x= 6 6. ( ) hx = x x + x + x 8; x= 7 7. ( ) 5 hx = 5x 7x + x f x = 8x x + In Exercises 8 and 9, describe the end behavior of the graph of the function. gx = 6x x + x + 8x+ 8. ( ) hx = 5x + 6x 5x + x 9. ( ) 9 7 In Exercises 0, graph the polnomial function. 0. qx ( ) = x. hx ( ) = x x+ 5. k( x) = x + x. f( x) x x = + In Exercises and 5, describe the x-values for which f is increasing, decreasing, positive, and negative.. f 5. f x x 6. Suppose f( x) as x and f( x) as x +. Describe the degree and leading coefficient of the function. 96 Algebra Copright Big Ideas Learning, LLC

2 Name Date. Practice A In Exercises, find the sum.. ( 6x + x 7) + ( 0x + x ). ( 0x + x 5x + ) + ( 7x 5 5x + x 9). ( 5x + x 6x 0) + ( x 7x + 6x + ) In Exercises 6, find the difference.. ( x + 6x 9x + ) ( 8x + x 5x ) 5. ( 0x x 7x + 5x + 9) ( x 5x x + 9x + ) 6. ( 7x 5 + x x + x + 5) ( 6x 9x + x ) 7. A cit is planning a new sports park. The total area (in square feet) of the park is modeled b the expression 9x + x 5. The area of the park designated for soccer fields is modeled b the expression x 5x +. Write an expression that models the area of the park that is not designated for soccer fields. In Exercises 8, find the product. 8. 5x ( x + 7x + 6) 9. x ( 0x 9x 7x + ) 0. ( 8x x )( x ) + +. ( x 6)( x + x + 9). Describe and correct the error in performing the operation. ( ) x x 5x + 7 = x 5x + x In Exercises 6, find the product of the binomials.. ( x )( x + )( x ). ( x 6)( x 9)( x + ) 5. ( x + )( x + )( x ) 6. ( x + 5)( x )( x + ) In Exercises 7 9, find the product. 7. ( x + 8)( x 8) 8. ( + ) 9. ( p ) Copright Big Ideas Learning, LLC Algebra 0

3 Name Date. Practice A In Exercises, divide using polnomial long division.. ( x + x + ) ( x 5). ( x x ) ( x ). ( x + x 9x 6) ( x 9). ( 6x x + x) ( x + ) In Exercises 5 0, divide using snthetic division. 5. ( x + 6x + ) ( x ) 6. ( x x ) ( x ) 7. ( x x + 5) ( x + ) 8. ( x x + 6 ) ( x + ) 9. ( x + 5 ) ( x 5 ) 0. ( 5x x + ) ( x ). Describe and correct the error in using snthetic division to divide x + x + 7 b x x + x = x + 5x x + x + In Exercises 5, use snthetic division to evaluate the function for the indicated value of x.. f( x) = x 7x + 8; x = f x = x x + 6; x = 5. ( ) f x = x + x x + ; x =. ( ) f x = x + x 5x + ; x = 5. ( ) 6. You divide two polnomials and obtain the result x the dividend? How did ou find it? +. What is x Algebra Copright Big Ideas Learning, LLC

4 Name Date. Practice A In Exercises 6, factor the polnomial completel.. x x x p 6p. n n + 7n k k 5. w 7w 5w 6.. q 7q 8q 6 5 In Exercises 7 9, factor the polnomial completel. 7. x w 5 In Exercises 0, factor the polnomial completel q q q d + 0d + d + 5. x 6x 9x + 5 In Exercises 6, factor the polnomial completel.. 6 p 5 5. n + n In Exercises 7 0, determine whether the binomial is a factor of the polnomial function. f x = x + 7x 8x 5; x ( ) f x = x + 5x x + 6; x ( ) f x = 6x 8x 6x x ; x 9. ( ) 5 f x = x 69x + 9x + 0; x 6 0. ( ). Fill in the blank of the divisor so that the remainder is 0. Justif our answer. ( ) = ; ( ) f x x x x x. What is the value of k such that x 6 is a factor of f x = x 7x kx + 8? Justif our answer. ( ). Factor each polnomial completel. 5ac ad+ 5bc bd a. n n b. x + 6x + 9 Copright Big Ideas Learning, LLC Algebra

5 Name Date.5 Practice A In Exercises 6, solve the equation.. q q 0q. k + 6k + 9k 6 =. n + n 9n p = p 6. 8u = 6u In Exercises 7 0, find the zeros of the function. Then sketch a graph of the function. 7. f ( x) = x + x x 8. gx ( ) x x = hx ( ) = x x 5x 0. ( ) f x = x 5x x. According to the Rational Root Theorem, which is not a possible solution of the equation x 6x + x +? A. B. C. D.. Describe and correct the error in listing the possible rational zeros of the function. Possible zeros: In Exercises and, find all the real solutions of the equation.. x 8x 9. x + x 5x 6 5. Write a third or fourth degree polnomial function that has zeros at ±. Justif our answer. 6. Determine the value of k for each equation so that the given x-value is a solution. x + x 9x + k ; x = a. x x + kx ; x = b. 6 Algebra Copright Big Ideas Learning, LLC

6 Name Date.6 Practice A In Exercises, identif the number of solutions or zeros. x + x x + x q q 7q =. 6r + r 7r In Exercises 5 8, find all zeros of the polnomial function. f x = x 5x 6 5. ( ) f x = x + x 7x x ( ) g x = x x + 9x 9x 7. ( ) hx = x x ( ) In Exercises 9 and 0, determine the number of imaginar zeros for the function with the given degree and graph. Explain our reasoning. 9. Degree: 5 0. Degree: 8 8 x 8 8 x 8 In Exercises, write a polnomial function f of least degree that has rational coefficients, a leading coefficient of, and the given zeros..,,.,,.,. Write a polnomial function of degree 5 with zeros,, and i. Justif our answer. In Exercises 5 7, determine the possible numbers of positive real zeros, negative real zeros, and imaginar zeros for the function. gx = x x x+ 5. ( ) 6. gx ( ) = x + x 0 gx = x x + x x 7. ( ) 5 Copright Big Ideas Learning, LLC Algebra

Lesson 7.1 Polynomial Degree and Finite Differences

Lesson 7.1 Polynomial Degree and Finite Differences Lesson 7.1 Polnomial Degree and Finite Differences 1. Identif the degree of each polnomial. a. 1 b. 0. 1. 3. 3 c. 0 16 0. Determine which of the epressions are polnomials. For each polnomial, state its

More information

Algebra II Practice Semester Exam Specification Sheet

Algebra II Practice Semester Exam Specification Sheet Algebra II Practice Semester Exam Specification Sheet 1. Properties of real numbers. Procedure (write procedure or process) 3. Concept development/linkage. Theorem/factual knowledge (of theorems and rules)

More information

Essential Question How can you determine whether a polynomial equation has imaginary solutions? 2 B. 4 D. 4 F.

Essential Question How can you determine whether a polynomial equation has imaginary solutions? 2 B. 4 D. 4 F. 5. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS 2A.7.A The Fundamental Theorem of Algebra Essential Question How can ou determine whether a polnomial equation has imaginar solutions? Cubic Equations and Imaginar

More information

Polynomial and Rational Functions

Polynomial and Rational Functions Name Date Chapter Polnomial and Rational Functions Section.1 Quadratic Functions Objective: In this lesson ou learned how to sketch and analze graphs of quadratic functions. Important Vocabular Define

More information

Factoring Polynomials

Factoring Polynomials 5. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS 2A.7.D 2A.7.E Factoring Polnomials Essential Question How can ou factor a polnomial? Factoring Polnomials Work with a partner. Match each polnomial equation with

More information

Downloaded from

Downloaded from Question 1: Exercise 2.1 The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case. (i) (ii) (iii) Page 1 of 24 (iv) (v) (v) Page

More information

5.4 dividing POlynOmIAlS

5.4 dividing POlynOmIAlS SECTION 5.4 dividing PolNomiAls 3 9 3 learning ObjeCTIveS In this section, ou will: Use long division to divide polnomials. Use snthetic division to divide polnomials. 5.4 dividing POlnOmIAlS Figure 1

More information

7.1 Practice A. w y represents the height of an object t seconds. Name Date

7.1 Practice A. w y represents the height of an object t seconds. Name Date Name Date 7.1 Practice A In Eercises 1 3, find the degree of the monomial. 3 1. 7n. 1 w 5 3 3. 5 In Eercises 4 6, write the polnomial in standard form. Identif the degree and leading coefficient of the

More information

2.1 Evaluate and Graph Polynomial

2.1 Evaluate and Graph Polynomial 2. Evaluate and Graph Polnomial Functions Georgia Performance Standard(s) MM3Ab, MM3Ac, MM3Ad Your Notes Goal p Evaluate and graph polnomial functions. VOCABULARY Polnomial Polnomial function Degree of

More information

Algebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions.

Algebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions. Algebra II Notes Unit Si: Polnomials Sllabus Objectives: 6. The student will simplif polnomial epressions. Review: Properties of Eponents (Allow students to come up with these on their own.) Let a and

More information

3 Polynomial and Rational Functions

3 Polynomial and Rational Functions 3 Polnomial and Rational Functions 3.1 Quadratic Functions and Models 3.2 Polnomial Functions and Their Graphs 3.3 Dividing Polnomials 3.4 Real Zeros of Polnomials 3.5 Comple Zeros and the Fundamental

More information

Chapter 9. Worked-Out Solutions. Check. Chapter 9 Maintaining Mathematical Proficiency (p. 477) y = 2 x 2. y = 1. = (x + 5) 2 4 =?

Chapter 9. Worked-Out Solutions. Check. Chapter 9 Maintaining Mathematical Proficiency (p. 477) y = 2 x 2. y = 1. = (x + 5) 2 4 =? Maintaining Mathematical Proficienc (p. ). x + 0x + x + (x)() + (x + ). x 0x + 00 x (x)(0) + 0 (x 0). x + x + x + (x)() + (x + ). x x + x (x)(9) + 9 (x 9). x + x + x + (x)() + (x + ) Check x x +? ()? ()

More information

Skills Practice Skills Practice for Lesson 10.1

Skills Practice Skills Practice for Lesson 10.1 Skills Practice Skills Practice for Lesson.1 Name Date Higher Order Polynomials and Factoring Roots of Polynomial Equations Problem Set Solve each polynomial equation using factoring. Then check your solution(s).

More information

CHAPTER 1-5 CREDIT INTERVENTION ASSIGNMENT

CHAPTER 1-5 CREDIT INTERVENTION ASSIGNMENT MHFU NAME: DATE: CHAPTER - CREDIT INTERVENTION ASSIGNMENT Circle the best option and write our choice in the space provided Show our work clearl and in the correct order on separate sheets Which one of

More information

MATH College Algebra Review for Test 2

MATH College Algebra Review for Test 2 MATH 4 - College Algebra Review for Test Sections. and.. For f (x) = x + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the axis of

More information

, a 1. , a 2. ,..., a n

, a 1. , a 2. ,..., a n CHAPTER Points to Remember :. Let x be a variable, n be a positive integer and a 0, a, a,..., a n be constants. Then n f ( x) a x a x... a x a, is called a polynomial in variable x. n n n 0 POLNOMIALS.

More information

Polynomial and Rational Functions

Polynomial and Rational Functions Polnomial and Rational Functions 5 Figure 1 35-mm film, once the standard for capturing photographic images, has been made largel obsolete b digital photograph. (credit film : modification of work b Horia

More information

171S4.3 Polynomial Division; The Remainder and Factor Theorems. October 26, Polynomial Division; The Remainder and Factor Theorems

171S4.3 Polynomial Division; The Remainder and Factor Theorems. October 26, Polynomial Division; The Remainder and Factor Theorems MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial

More information

171S4.3 Polynomial Division; The Remainder and Factor Theorems. March 24, Polynomial Division; The Remainder and Factor Theorems

171S4.3 Polynomial Division; The Remainder and Factor Theorems. March 24, Polynomial Division; The Remainder and Factor Theorems MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial

More information

Factoring Review WS 3.0. Factoring Polynomials Factor and Remainder Theorems. Factoring a Sum or Difference of Cubes Pg. 182 # 1-5

Factoring Review WS 3.0. Factoring Polynomials Factor and Remainder Theorems. Factoring a Sum or Difference of Cubes Pg. 182 # 1-5 UNIT POLYNOMIAL FUNCTIONS Date Lesson Text TOPIC Homework Sept. 0.0.0 Factoring Review WS.0 Sept. 1.1.5 Dividing Polnomials Pg. 168 #,, 4, (5 10)doso, 11, 1 Sept...6 Factoring Polnomials Factor and Remainder

More information

Question 1: The graphs of y = p(x) are given in following figure, for some Polynomials p(x). Find the number of zeroes of p(x), in each case.

Question 1: The graphs of y = p(x) are given in following figure, for some Polynomials p(x). Find the number of zeroes of p(x), in each case. Class X - NCERT Maths EXERCISE NO:.1 Question 1: The graphs of y = p(x) are given in following figure, for some Polynomials p(x). Find the number of zeroes of p(x), in each case. (i) (ii) (iii) (iv) (v)

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Chapter Maintaining Mathematical Proficiency Simplify the expression. 1. 8x 9x 2. 25r 5 7r r + 3. 3 ( 3x 5) + + x. 3y ( 2y 5) + 11 5. 3( h 7) 7( 10 h) 2 2 +. 5 8x + 5x + 8x Find the volume or surface area

More information

Copyrighted by Gabriel Tang B.Ed., B.Sc. Page 111.

Copyrighted by Gabriel Tang B.Ed., B.Sc. Page 111. Algera Chapter : Polnomial and Rational Functions Chapter : Polnomial and Rational Functions - Polnomial Functions and Their Graphs Polnomial Functions: - a function that consists of a polnomial epression

More information

Fair Game Review. Chapter 9. Find the square root(s) ± Find the side length of the square. 7. Simplify Simplify 63.

Fair Game Review. Chapter 9. Find the square root(s) ± Find the side length of the square. 7. Simplify Simplify 63. Name Date Chapter 9 Find the square root(s). Fair Game Review... 9. ±. Find the side length of the square.. s. s s Area = 9 ft s Area = 0. m 7. Simplif 0. 8. Simplif. 9. Simplif 08. 0. Simplif 88. Copright

More information

Unit 1: Polynomial Functions SuggestedTime:14 hours

Unit 1: Polynomial Functions SuggestedTime:14 hours Unit 1: Polynomial Functions SuggestedTime:14 hours (Chapter 3 of the text) Prerequisite Skills Do the following: #1,3,4,5, 6a)c)d)f), 7a)b)c),8a)b), 9 Polynomial Functions A polynomial function is an

More information

2.6. Graphs of Rational Functions. Copyright 2011 Pearson, Inc.

2.6. Graphs of Rational Functions. Copyright 2011 Pearson, Inc. 2.6 Graphs of Rational Functions Copyright 2011 Pearson, Inc. Rational Functions What you ll learn about Transformations of the Reciprocal Function Limits and Asymptotes Analyzing Graphs of Rational Functions

More information

f(x) = 2x 2 + 2x - 4

f(x) = 2x 2 + 2x - 4 4-1 Graphing Quadratic Functions What You ll Learn Scan the tet under the Now heading. List two things ou will learn about in the lesson. 1. Active Vocabular 2. New Vocabular Label each bo with the terms

More information

L1 2.1 Long Division of Polynomials and The Remainder Theorem Lesson MHF4U Jensen

L1 2.1 Long Division of Polynomials and The Remainder Theorem Lesson MHF4U Jensen L1 2.1 Long Division of Polynomials and The Remainder Theorem Lesson MHF4U Jensen In this section you will apply the method of long division to divide a polynomial by a binomial. You will also learn to

More information

Fair Game Review. Chapter 10

Fair Game Review. Chapter 10 Name Date Chapter 0 Evaluate the expression. Fair Game Review. 9 +. + 6. 8 +. 9 00. ( 9 ) 6. 6 ( + ) 7. 6 6 8. 9 6 x 9. The number of visits to a website can be modeled b = +, where is hundreds of visits

More information

Ready To Go On? Skills Intervention 6-1 Polynomials

Ready To Go On? Skills Intervention 6-1 Polynomials 6A Read To Go On? Skills Intervention 6- Polnomials Find these vocabular words in Lesson 6- and the Multilingual Glossar. Vocabular monomial polnomial degree of a monomial degree of a polnomial leading

More information

Review for Midterm Exam

Review for Midterm Exam Algebra Name n ]0\sD tkkustsaf ASPoRfrtfwZaArHep clzldcg.q L maflnlp orbitgjhxtlsr LrmeesaecrbvFedk. Review for Midterm Eam Graph each line. Date ) = + ) + 5 = 0 5 5-5 - Find the inverse of the linearfunction.

More information

Pre-Algebra 2. Unit 9. Polynomials Name Period

Pre-Algebra 2. Unit 9. Polynomials Name Period Pre-Algebra Unit 9 Polynomials Name Period 9.1A Add, Subtract, and Multiplying Polynomials (non-complex) Explain Add the following polynomials: 1) ( ) ( ) ) ( ) ( ) Subtract the following polynomials:

More information

Chapter 3: Polynomial and Rational Functions

Chapter 3: Polynomial and Rational Functions Chapter 3: Polynomial and Rational Functions 3.1 Polynomial Functions and Their Graphs A polynomial function of degree n is a function of the form P (x) = a n x n + a n 1 x n 1 + + a 1 x + a 0 The numbers

More information

Bell Quiz 2-3. Determine the end behavior of the graph using limit notation. Find a function with the given zeros , 2. 5 pts possible.

Bell Quiz 2-3. Determine the end behavior of the graph using limit notation. Find a function with the given zeros , 2. 5 pts possible. Bell Quiz 2-3 2 pts Determine the end behavior of the graph using limit notation. 5 2 1. g( ) = 8 + 13 7 3 pts Find a function with the given zeros. 4. -1, 2 5 pts possible Ch 2A Big Ideas 1 Questions

More information

LESSON #28 - POWER FUNCTIONS COMMON CORE ALGEBRA II

LESSON #28 - POWER FUNCTIONS COMMON CORE ALGEBRA II 1 LESSON #8 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The

More information

2.1. The Remainder Theorem. How do you divide using long division?

2.1. The Remainder Theorem. How do you divide using long division? .1 The Remainder Theorem A manufacturer of cardboard boxes receives an order for gift boxes. Based on cost calculations, the volume, V, of each box to be constructed can be modelled by the polynomial function

More information

L1 2.1 Long Division of Polynomials and The Remainder Theorem Lesson MHF4U Jensen

L1 2.1 Long Division of Polynomials and The Remainder Theorem Lesson MHF4U Jensen L1 2.1 Long Division of Polynomials and The Remainder Theorem Lesson MHF4U Jensen In this section you will apply the method of long division to divide a polynomial by a binomial. You will also learn to

More information

Polynomial and Synthetic Division

Polynomial and Synthetic Division Polynomial and Synthetic Division Polynomial Division Polynomial Division is very similar to long division. Example: 3x 3 5x 3x 10x 1 3 Polynomial Division 3x 1 x 3x 3 3 x 5x 3x x 6x 4 10x 10x 7 3 x 1

More information

MATH College Algebra Review for Test 2

MATH College Algebra Review for Test 2 MATH 34 - College Algebra Review for Test 2 Sections 3. and 3.2. For f (x) = x 2 + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the

More information

CHAPTER 2 Polynomial and Rational Functions

CHAPTER 2 Polynomial and Rational Functions CHAPTER Polnomial and Rational Functions Section. Quadratic Functions..................... 9 Section. Polnomial Functions of Higher Degree.......... Section. Real Zeros of Polnomial Functions............

More information

Dividing Polynomials

Dividing Polynomials 5.3 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS 2A.7.C Dividing Polynomials Essential Question How can you use the factors of a cubic polynomial to solve a division problem involving the polynomial? Dividing

More information

Lesson 2.1: Quadratic Functions

Lesson 2.1: Quadratic Functions Quadratic Functions: Lesson 2.1: Quadratic Functions Standard form (vertex form) of a quadratic function: Vertex: (h, k) Algebraically: *Use completing the square to convert a quadratic equation into standard

More information

Name Date. Work with a partner. Each graph shown is a transformation of the parent function

Name Date. Work with a partner. Each graph shown is a transformation of the parent function 3. Transformations of Eponential and Logarithmic Functions For use with Eploration 3. Essential Question How can ou transform the graphs of eponential and logarithmic functions? 1 EXPLORATION: Identifing

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter 8 Maintaining Mathematical Proficienc Graph the linear equation. 1. = 5. = + 3 3. 1 = + 3. = + Evaluate the epression when =. 5. + 8. + 3 7. 3 8. 5 + 8 9. 8 10. 5 + 3 11. + + 1. 3 + +

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

Dividing Polynomials: Remainder and Factor Theorems

Dividing Polynomials: Remainder and Factor Theorems Dividing Polynomials: Remainder and Factor Theorems When we divide one polynomial by another, we obtain a quotient and a remainder. If the remainder is zero, then the divisor is a factor of the dividend.

More information

Polynomials. Exponents. End Behavior. Writing. Solving Factoring. Graphing. End Behavior. Polynomial Notes. Synthetic Division.

Polynomials. Exponents. End Behavior. Writing. Solving Factoring. Graphing. End Behavior. Polynomial Notes. Synthetic Division. Polynomials Polynomials 1. P 1: Exponents 2. P 2: Factoring Polynomials 3. P 3: End Behavior 4. P 4: Fundamental Theorem of Algebra Writing real root x= 10 or (x+10) local maximum Exponents real root x=10

More information

Ready To Go On? Skills Intervention 12-1 Inverse Variation

Ready To Go On? Skills Intervention 12-1 Inverse Variation 12A Find this vocabular word in Lesson 12-1 and the Multilingual Glossar. Identifing Inverse Variation Tell whether the relationship is an inverse variation. Eplain. A. Read To Go On? Skills Intervention

More information

LESSON #24 - POWER FUNCTIONS COMMON CORE ALGEBRA II

LESSON #24 - POWER FUNCTIONS COMMON CORE ALGEBRA II 1 LESSON #4 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The

More information

Chapter 3 Polynomial Functions

Chapter 3 Polynomial Functions Trig / Coll. Alg. Name: Chapter 3 Polynomial Functions 3.1 Quadratic Functions (not on this test) For each parabola, give the vertex, intercepts (x- and y-), axis of symmetry, and sketch the graph. 1.

More information

Fair Game Review. Chapter of a mile the next day. How. far will you jog over the next two days? How many servings does the

Fair Game Review. Chapter of a mile the next day. How. far will you jog over the next two days? How many servings does the Name Date Chapter Evaluate the epression.. Fair Game Review 5 +. 3 3 7 3 8 4 3. 4 4. + 5 0 5 6 5. 3 6. 4 6 5 4 6 3 7. 5 8. 3 9 8 4 3 5 9. You plan to jog 3 4 of a mile tomorrow and 7 8 of a mile the net

More information

Unit 5 Evaluation. Multiple-Choice. Evaluation 05 Second Year Algebra 1 (MTHH ) Name I.D. Number

Unit 5 Evaluation. Multiple-Choice. Evaluation 05 Second Year Algebra 1 (MTHH ) Name I.D. Number Name I.D. Number Unit Evaluation Evaluation 0 Second Year Algebra (MTHH 039 09) This evaluation will cover the lessons in this unit. It is open book, meaning you can use your textbook, syllabus, and other

More information

b) since the remainder is 0 I need to factor the numerator. Synthetic division tells me this is true

b) since the remainder is 0 I need to factor the numerator. Synthetic division tells me this is true Section 5.2 solutions #1-10: a) Perform the division using synthetic division. b) if the remainder is 0 use the result to completely factor the dividend (this is the numerator or the polynomial to the

More information

ZEROS OF POLYNOMIAL FUNCTIONS ALL I HAVE TO KNOW ABOUT POLYNOMIAL FUNCTIONS

ZEROS OF POLYNOMIAL FUNCTIONS ALL I HAVE TO KNOW ABOUT POLYNOMIAL FUNCTIONS ZEROS OF POLYNOMIAL FUNCTIONS ALL I HAVE TO KNOW ABOUT POLYNOMIAL FUNCTIONS TOOLS IN FINDING ZEROS OF POLYNOMIAL FUNCTIONS Synthetic Division and Remainder Theorem (Compressed Synthetic Division) Fundamental

More information

Using Properties of Exponents

Using Properties of Exponents 6.1 Using Properties of Exponents Goals p Use properties of exponents to evaluate and simplify expressions involving powers. p Use exponents and scientific notation to solve real-life problems. VOCABULARY

More information

Test # 2 Review Sections (2.4,2.5,2.6, & ch. 3) Math 1314 Name

Test # 2 Review Sections (2.4,2.5,2.6, & ch. 3) Math 1314 Name Test # Review Sections (.,.,., & ch. 3) Math 131 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the equation of the line. 1) -intercept,

More information

Rational Equations. You can use a rational function to model the intensity of sound.

Rational Equations. You can use a rational function to model the intensity of sound. UNIT Rational Equations You can use a rational function to model the intensit of sound. Copright 009, K Inc. All rights reserved. This material ma not be reproduced in whole or in part, including illustrations,

More information

Algebra 2 Semester Exam Review

Algebra 2 Semester Exam Review Algebra Semester Eam Review 7 Graph the numbers,,,, and 0 on a number line Identif the propert shown rs rs r when r and s Evaluate What is the value of k k when k? Simplif the epression 7 7 Solve the equation

More information

Lesson 7.1 Polynomial Degree and Finite Differences

Lesson 7.1 Polynomial Degree and Finite Differences Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 3x 4 2x 3 3x 2 x 7 b. x 1 c. 0.2x 1.x 2 3.2x 3 d. 20 16x 2 20x e. x x 2 x 3 x 4 x f. x 2 6x 2x 6 3x 4 8

More information

Rewriting Absolute Value Functions as Piece-wise Defined Functions

Rewriting Absolute Value Functions as Piece-wise Defined Functions Rewriting Absolute Value Functions as Piece-wise Defined Functions Consider the absolute value function f ( x) = 2x+ 4-3. Sketch the graph of f(x) using the strategies learned in Algebra II finding the

More information

4.3 Division of Polynomials

4.3 Division of Polynomials 4.3 Division of Polynomials Learning Objectives Divide a polynomials by a monomial. Divide a polynomial by a binomial. Rewrite and graph rational functions. Introduction A rational epression is formed

More information

SEE the Big Idea. Quonset Hut (p. 218) Zebra Mussels (p. 203) Ruins of Caesarea (p. 195) Basketball (p. 178) Electric Vehicles (p.

SEE the Big Idea. Quonset Hut (p. 218) Zebra Mussels (p. 203) Ruins of Caesarea (p. 195) Basketball (p. 178) Electric Vehicles (p. Polnomial Functions.1 Graphing Polnomial Functions. Adding, Subtracting, and Multipling Polnomials.3 Dividing Polnomials. Factoring Polnomials.5 Solving Polnomial Equations. The Fundamental Theorem of

More information

3.4 The Fundamental Theorem of Algebra

3.4 The Fundamental Theorem of Algebra 333371_0304.qxp 12/27/06 1:28 PM Page 291 3.4 The Fundamental Theorem of Algebra Section 3.4 The Fundamental Theorem of Algebra 291 The Fundamental Theorem of Algebra You know that an nth-degree polynomial

More information

Section 0.2 & 0.3 Worksheet. Types of Functions

Section 0.2 & 0.3 Worksheet. Types of Functions MATH 1142 NAME Section 0.2 & 0.3 Worksheet Types of Functions Now that we have discussed what functions are and some of their characteristics, we will explore different types of functions. Section 0.2

More information

Power and Polynomial Functions. College Algebra

Power and Polynomial Functions. College Algebra Power and Polynomial Functions College Algebra Power Function A power function is a function that can be represented in the form f x = kx % where k and p are real numbers, and k is known as the coefficient.

More information

Lesson 7.1 Polynomial Degree and Finite Differences

Lesson 7.1 Polynomial Degree and Finite Differences Lesson 7.1 Polynomial Degree and Finite Differences 1. Identify the degree of each polynomial. a. 1 b. 0.2 1. 2 3.2 3 c. 20 16 2 20 2. Determine which of the epressions are polynomials. For each polynomial,

More information

5.1 Practice A. Name Date ( ) 23 15, , x = 20. ( ) 2

5.1 Practice A. Name Date ( ) 23 15, , x = 20. ( ) 2 Name Date. Practice A In Exercises, find the indicated real nth root(s) of a.. n =, a =. n =, a = 9. n =, a = 8 In Exercises 9, evaluate the expression without using a calculator.. 7. 6 8. ( ) 7. 6 6.

More information

Need help? Try or 4.1 Practice Problems

Need help? Try  or  4.1 Practice Problems Day Date Assignment (Due the next class meeting) Friday 9/29/17 (A) Monday 10/9/17 (B) 4.1 Operations with polynomials Tuesday 10/10/17 (A) Wednesday 10/11/17 (B) 4.2 Factoring and solving completely Thursday

More information

2 nd Semester Final Exam Review Block Date

2 nd Semester Final Exam Review Block Date Algebra 1B Name nd Semester Final Eam Review Block Date Calculator NOT Allowed Graph each function. Identif the verte and ais of smmetr. 1 (10-1) 1. (10-1). 3 (10-) 3. 4 7 (10-) 4. 3 6 4 (10-1) 5. Predict

More information

2 nd Semester Final Exam Review Block Date

2 nd Semester Final Exam Review Block Date Algebra 1B Name nd Semester Final Eam Review Block Date Calculator NOT Allowed Graph each function. 1 (10-1) 1. (10-1). (10-1) 3. (10-1) 4. 3 Graph each function. Identif the verte, ais of smmetr, and

More information

d. 2x 3 7x 2 5x 2 2x 2 3x 1 x 2x 3 3x 2 1x 2 4x 2 6x 2 3. a. x 5 x x 2 5x 5 5x 25 b. x 4 2x 2x 2 8x 3 3x 12 c. x 6 x x 2 6x 6 6x 36

d. 2x 3 7x 2 5x 2 2x 2 3x 1 x 2x 3 3x 2 1x 2 4x 2 6x 2 3. a. x 5 x x 2 5x 5 5x 25 b. x 4 2x 2x 2 8x 3 3x 12 c. x 6 x x 2 6x 6 6x 36 Vertices: (.8, 5.), (.37, 3.563), (.6, 0.980), (5.373, 6.66), (.8, 7.88), (.95,.) Graph the equation for an value of P (the second graph shows the circle with P 5) and imagine increasing the value of P,

More information

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i Final Exam C Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 7 ) x + + 3 x - = 6 (x + )(x - ) ) A) No restrictions; {} B) x -, ; C) x -; {} D) x -, ; {2} Add

More information

FINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name

FINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name FINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name 1) Find the SUM of the solutions of the equation. 82 + 0 = 16 Use the quadratic formula to solve the equation. (All solutions are real numbers.)

More information

Chapter 8. Exploring Polynomial Functions. Jennifer Huss

Chapter 8. Exploring Polynomial Functions. Jennifer Huss Chapter 8 Exploring Polynomial Functions Jennifer Huss 8-1 Polynomial Functions The degree of a polynomial is determined by the greatest exponent when there is only one variable (x) in the polynomial Polynomial

More information

6x 3 12x 2 7x 2 +16x 7x 2 +14x 2x 4

6x 3 12x 2 7x 2 +16x 7x 2 +14x 2x 4 2.3 Real Zeros of Polynomial Functions Name: Pre-calculus. Date: Block: 1. Long Division of Polynomials. We have factored polynomials of degree 2 and some specific types of polynomials of degree 3 using

More information

BIG IDEAS MATH. Ron Larson Laurie Boswell. Sampler

BIG IDEAS MATH. Ron Larson Laurie Boswell. Sampler BIG IDEAS MATH Ron Larson Laurie Boswell Sampler 3 Polnomial Functions 3.1 Graphing Polnomial Functions 3. Adding, Subtracting, and Multipling Polnomials 3.3 Dividing Polnomials 3. Factoring Polnomials

More information

Chapter 2 Polynomial and Rational Functions

Chapter 2 Polynomial and Rational Functions Chapter 2 Polynomial and Rational Functions Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Quadratic Functions Polynomial Functions of Higher Degree Real Zeros of Polynomial Functions

More information

MATHEMATICAL METHODS UNIT 1 CHAPTER 4 CUBIC POLYNOMIALS

MATHEMATICAL METHODS UNIT 1 CHAPTER 4 CUBIC POLYNOMIALS E da = q ε ( B da = 0 E ds = dφ. B ds = μ ( i + μ ( ε ( dφ 3 MATHEMATICAL METHODS UNIT 1 CHAPTER 4 CUBIC POLYNOMIALS dt dt Key knowledge The key features and properties of cubic polynomials functions and

More information

Algebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology.

Algebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology. Sllabus Objectives:.1 The student will graph quadratic functions with and without technolog. Quadratic Function: a function that can be written in the form are real numbers Parabola: the U-shaped graph

More information

How many solutions are real? How many solutions are imaginary? What are the solutions? (List below):

How many solutions are real? How many solutions are imaginary? What are the solutions? (List below): 1 Algebra II Chapter 5 Test Review Standards/Goals: F.IF.7.c: I can identify the degree of a polynomial function. F.1.a./A.APR.1.: I can evaluate and simplify polynomial expressions and equations. F.1.b./

More information

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH 05 Review Sheet

BRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH 05 Review Sheet BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH 05 Review Sheet Go to http://www.cun.edu/testing for more information on the CUNY Elementar Algebra

More information

Polynomial Review Problems

Polynomial Review Problems Polynomial Review Problems 1. Find polynomial function formulas that could fit each of these graphs. Remember that you will need to determine the value of the leading coefficient. The point (0,-3) is on

More information

Copyright PreCalculusCoach.com

Copyright PreCalculusCoach.com Continuit, End Behavior, and Limits Assignment Determine whether each function is continuous at the given -values. Justif using the continuit test. If discontinuous, identif the tpe of discontinuit as

More information

3.4. ZEROS OF POLYNOMIAL FUNCTIONS

3.4. ZEROS OF POLYNOMIAL FUNCTIONS 3.4. ZEROS OF POLYNOMIAL FUNCTIONS What You Should Learn Use the Fundamental Theorem of Algebra to determine the number of zeros of polynomial functions. Find rational zeros of polynomial functions. Find

More information

Final Exam Review Spring a. Is this a quadratic? 2 a. Is this a quadratic? b. EXPLAIN why or why not. b. EXPLAIN why or why not!!

Final Exam Review Spring a. Is this a quadratic? 2 a. Is this a quadratic? b. EXPLAIN why or why not. b. EXPLAIN why or why not!! Final Exam Review Spring 01-013 Name Module 4 Fill in the charts below. x x -6 0 Change in 0 0 Change in -3 1 1-1 4 5 0 9 3 10 16 4 17 5 5 5 6 6 36 6 37 1 Is this a quadratic? Is this a quadratic? b. EXPLAIN

More information

N x. You should know how to decompose a rational function into partial fractions.

N x. You should know how to decompose a rational function into partial fractions. Section 7. Partial Fractions 0. 0 7 0 0 0 0 Solution:, 0 Equation Equation Eq. Eq. 07. nswers will var. Section 7. Partial Fractions N You should know how to decompose a rational function into partial

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter 3 Maintaining Mathematical Proficienc Plot the point in a coordinate plane. Describe the location of the point. 1. A( 3, 1). B (, ) 3. C ( 1, 0). D ( 5, ) 5. Plot the point that is on

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter Maintaining Mathematical Proficienc Use the graph to answer the question. A H B F G E C D x 1. What ordered pair corresponds to point A?. What ordered pair corresponds to point H? 3.

More information

Cumulative Review. Name. 13) 2x = -4 13) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Cumulative Review. Name. 13) 2x = -4 13) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Cumulative Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the algebraic expression for the given value or values of the variable(s).

More information

Learning Goals. College of Charleston Department of Mathematics Math 101: College Algebra Final Exam Review Problems 1

Learning Goals. College of Charleston Department of Mathematics Math 101: College Algebra Final Exam Review Problems 1 College of Charleston Department of Mathematics Math 0: College Algebra Final Eam Review Problems Learning Goals (AL-) Arithmetic of Real and Comple Numbers: I can classif numbers as natural, integer,

More information

Class IX Chapter 2 Polynomials Maths

Class IX Chapter 2 Polynomials Maths NCRTSOLUTIONS.BLOGSPOT.COM Class IX Chapter 2 Polynomials Maths Exercise 2.1 Question 1: Which of the following expressions are polynomials in one variable and which are No. It can be observed that the

More information

REVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES

REVIEW KEY VOCABULARY REVIEW EXAMPLES AND EXERCISES Etra Eample. Graph.. 6. 7. (, ) (, ) REVIEW KEY VOCABULARY quadratic function, p. 6 standard form of a quadratic function, p. 6 parabola, p. 6 verte, p. 6 ais of smmetr, p. 6 minimum, maimum value, p.

More information

Note: The actual exam will consist of 20 multiple choice questions and 6 show-your-work questions. Extra questions are provided for practice.

Note: The actual exam will consist of 20 multiple choice questions and 6 show-your-work questions. Extra questions are provided for practice. College Algebra - Unit 2 Exam - Practice Test Note: The actual exam will consist of 20 multiple choice questions and 6 show-your-work questions. Extra questions are provided for practice. MULTIPLE CHOICE.

More information

3 UNIT 4: QUADRATIC FUNCTIONS -- NO CALCULATOR

3 UNIT 4: QUADRATIC FUNCTIONS -- NO CALCULATOR Name: Algebra Final Exam Review, Part 3 UNIT 4: QUADRATIC FUNCTIONS -- NO CALCULATOR. Solve each of the following equations. Show your steps and find all solutions. a. 3x + 5x = 0 b. x + 5x - 9 = x + c.

More information

MAT 116 Final Exam Review

MAT 116 Final Exam Review MAT 116 Final Eam Review 1. Determine the equation for the line described, writing the answer in slope-intercept form. The line is parallel to = 8 and passes through ( 1,9). The line is perpendicular to

More information

Operations w/polynomials 4.0 Class:

Operations w/polynomials 4.0 Class: Exponential LAWS Review NO CALCULATORS Name: Operations w/polynomials 4.0 Class: Topic: Operations with Polynomials Date: Main Ideas: Assignment: Given: f(x) = x 2 6x 9 a) Find the y-intercept, the equation

More information

Test 2 Review Math 1111 College Algebra

Test 2 Review Math 1111 College Algebra Test 2 Review Math 1111 College Algebra 1. Begin by graphing the standard quadratic function f(x) = x 2. Then use transformations of this graph to graph the given function. g(x) = x 2 + 2 *a. b. c. d.

More information

Name Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit!

Name Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit! Name Period Date Practice FINAL EXAM Intro to Calculus (0 points) Show all work on separate sheet of paper for full credit! ) Evaluate the algebraic epression for the given value or values of the variable(s).

More information

Section Properties of Rational Expressions

Section Properties of Rational Expressions 88 Section. - Properties of Rational Expressions Recall that a rational number is any number that can be written as the ratio of two integers where the integer in the denominator cannot be. Rational Numbers:

More information

Polynomial Functions and Models

Polynomial Functions and Models 1 CA-Fall 2011-Jordan College Algebra, 4 th edition, Beecher/Penna/Bittinger, Pearson/Addison Wesley, 2012 Chapter 4: Polynomial Functions and Rational Functions Section 4.1 Polynomial Functions and Models

More information