Size: px
Start display at page:

Transcription

1 ID : ae-8-factorisation [1] Grade 8 Factorisation For more such worksheets visit Answer the questions (1) Find factors of following polynomial A) y 2-2xy + 3y - 6x B) 3y 2-12xy - 2y + 8x (2) Factorize (49z 2-100). (3) Write the following polynomials in factored form. A) 8xy + 6x 2 y 2 z 3 B) 16a 3 c + 72bc C) 32a 3 b a 2 bc D) 20x 2 yz yz 3 (4) Write the following polynomials in factored form: A) 30p 2 q p 2 q 4 B) 28p 3 q + 8p 2 q 3 C) 44xy xy 3 D) 45x 3 y x 2 y 2 (5) Find factors of polynomial (a 2-4ab + 4b 2-4c 2 ). (6) Factorize (4x + 7) 2-112x. (7) Find factors of following polynomial A) 45xy + 35y + 63x + 49 B) 3xy - 21y + 5x - 35 (8) Factorize (16y 2-40y + 25). (9) Find factors of following polynomial A) p 2 + 7p + 10 B) 5b 2-18b - 8 (10) Factorize (625x 4-200x ) Edugain ( All Rights Reserved Many more such worksheets can be generated at

2 Answers ID : ae-8-factorisation [2] (1) A) (y + 3)(y - 2x) Re-order some of the terms as following, y 2-2xy + 3y - 6x = y 2 + 3y - 2xy - 6x Now we can see that y is common in first two terms, and -2x is common in last two terms. Lets rewrite the expression as following, = y(y + 3) -2x(y + 3) = (y + 3)(y - 2x) Thus, the factors of the polynomial, y 2-2xy + 3y - 6x are (y - 2x)( y + 3). B) (3y - 2)(y - 4x) Re-order some of the terms as following, 3y 2-12xy - 2y + 8x = 3y 2-2y - 12xy + 8x Now we can see that y is common in first two terms, and -4x is common in last two terms. Lets rewrite the expression as following, = y(3y - 2) -4x(3y - 2) = (3y - 2)(y - 4x) Thus, the factors of the polynomial, 3y 2-12xy - 2y + 8x are (y - 4x)( 3y - 2). (2) (7z + 10) (7z - 10) We know that, a 2 - b 2 = (a + b)(a - b). Let's write (49z 2-100) as: (7z) 2 - (10) 2 = (7z + 10)(7z - 10)

3 ID : ae-8-factorisation [3] (3) A) 2xy(4 + 3xyz 3 ) If we look at the given polynomial carefully, we observe that 2xy is common to both the terms. By taking out the common factor 2xy from the polynomial 8xy + 6x 2 y 2 z 3, we get: 2xy(4 + 3xyz 3 ) Thus, the polynomial 8xy + 6x 2 y 2 z 3 can be written in the factored form as 2xy(4 + 3xyz 3 ). B) 8c(2a 3 + 9b) If we look at the given polynomial carefully, we observe that 8c is common to both the terms. By taking out the common factor 8c from the polynomial 16a 3 c + 72bc, we get: 8c(2a 3 + 9b) Thus, the polynomial 16a 3 c + 72bc can be written in the factored form as 8c(2a 3 + 9b). C) 16a 2 b(2ab + 3c) If we look at the given polynomial carefully, we observe that 16a 2 b is common to both the terms. By taking out the common factor 16a 2 b from the polynomial 32a 3 b a 2 bc, we get: 16a 2 b(2ab + 3c) Thus, the polynomial 32a 3 b a 2 bc can be written in the factored form as 16a 2 b(2ab + 3c).

4 ID : ae-8-factorisation [4] D) 20yz 3 (x 2 + 1) If we look at the given polynomial carefully, we observe that 20yz 3 is common to both the terms. By taking out the common factor 20yz 3 from the polynomial 20x 2 yz yz 3, we get: 20yz 3 (x 2 + 1) Thus, the polynomial 20x 2 yz yz 3 can be written in the factored form as 20yz 3 (x 2 + 1). (4) A) 30p 2 q 3 (1 + q) If we look at the given polynomial carefully, we observe that the factor 30p 2 q 3 is common to both terms of the polynomial 30p 2 q p 2 q 4. By taking out the common factor 30p 2 q 3 from the polynomial 30p 2 q p 2 q 4, we get the following factorization: 30p 2 q p 2 q 4 = 30p 2 q 3 (1 + q) Thus, the polynomial 30p 2 q p 2 q 4 can be written in factored form as 30p 2 q 3 (1 + q). B) 4p 2 q(7p + 2q 2 ) If we look at the given polynomial carefully, we observe that the factor 4p 2 q is common to both terms of the polynomial 28p 3 q + 8p 2 q 3. By taking out the common factor 4p 2 q from the polynomial 28p 3 q + 8p 2 q 3, we get the following factorization: 28p 3 q + 8p 2 q 3 = 4p 2 q(7p + 2q 2 ) Thus, the polynomial 28p 3 q + 8p 2 q 3 can be written in factored form as 4p 2 q(7p + 2q 2 ).

5 ID : ae-8-factorisation [5] C) 22xy 2 (2 + y) If we look at the given polynomial carefully, we observe that the factor 22xy 2 is common to both terms of the polynomial 44xy xy 3. By taking out the common factor 22xy 2 from the polynomial 44xy xy 3, we get the following factorization: 44xy xy 3 = 22xy 2 (2 + y) Thus, the polynomial 44xy xy 3 can be written in factored form as 22xy 2 (2 + y). D) 5x 2 y 2 (9x + 4) If we look at the given polynomial carefully, we observe that the factor 5x 2 y 2 is common to both terms of the polynomial 45x 3 y x 2 y 2. By taking out the common factor 5x 2 y 2 from the polynomial 45x 3 y x 2 y 2, we get the following factorization: 45x 3 y x 2 y 2 = 5x 2 y 2 (9x + 4) Thus, the polynomial 45x 3 y x 2 y 2 can be written in factored form as 5x 2 y 2 (9x + 4). (5) (a - 2b + 2c) (a - 2b - 2c) We know that, (a - b) 2 = a 2-2ab + b 2, a 2 - b 2 = (a + b)(a - b) The factors of the polynomial (a 2-4ab + 4b 2-4c 2 ) can be found using above identities as following, a 2-4ab + 4b 2-4c 2 = {(a) 2-4ab + (2b) 2 } - (2c) 2 = (a - 2b) 2 - (2c) 2 = (a - 2b + 2c) (a - 2b - 2c)

6 (6) (4x - 7) (4x - 7) ID : ae-8-factorisation [6] Using algebraic identity (a + b) 2 = a 2 + 2ab + b 2 (4x + 7) 2-112x = (4x) x + (7) 2-112x (4x + 7) 2-112x = (4x) 2-56x + (7) 2 (4x + 7) 2-112x = (4x) 2-2(7)(4x) + (7) 2 Now using algebraic identity (a - b) 2 = a 2-2ab + b 2 (4x + 7) 2-112x = (4x - 7) 2 (4x + 7) 2-112x = (4x - 7) (4x - 7) (7) A) (9x + 7)(5y + 7) The factors of the polynomial, 45xy + 35y + 63x + 49 can be found as, 45xy + 35y + 63x + 49 = 5y(9x + 7) + 7(9x + 7) = (9x + 7)(5y + 7) Thus, the factors of the polynomial, 45xy + 35y + 63x + 49 are ( 9x + 7)(5y + 7). B) (x - 7)(3y + 5) The factors of the polynomial, 3xy - 21y + 5x - 35 can be found as, 3xy - 21y + 5x - 35 = 3y(x - 7) + 5(x - 7) = (x - 7)(3y + 5) Thus, the factors of the polynomial, 3xy - 21y + 5x - 35 are ( x - 7)(3y + 5). (8) (4y - 5) 2 We know that, (a - b) 2 = a 2-2ab + b 2. (16y 2-40y + 25) can be factorized as, 16y 2-40y + 25 = (4y) 2-2(5)(4y) + (5) 2 = (4y - 5) 2

7 (9) A) (p + 5)(p + 2) ID : ae-8-factorisation [7] In order to find factors of polynomial p 2 + 7p + 10, we need to find two numbers whose sum is 7 and product is (10 1 = 10) We notice that 5 and 2 are such numbers, since (5) (2) = 10, and (5) + (2) = 7 Now we can re-write polynomial as following, p 2 + 7p + 10 = p 2 + 5p + 2p + 10 = p(p + 5) + 2(p + 5) = (p + 5)(p + 2) Step 4 Thus, the factors of the polynomial p 2 + 7p + 10 are (p + 5) and (p + 2). B) (5b + 2)(b - 4) In order to find factors of polynomial 5b 2-18b - 8, we need to find two numbers whose sum is -18 and product is (-8 5 = -40) We notice that 2 and -20 are such numbers, since (2) (-20) = -40, and (2) + (-20) = - 18 Now we can re-write polynomial as following, 5b 2-18b - 8 = 5b 2 + 2b - 20b - 8 = b(5b + 2) -4(5b + 2) = (5b + 2)(b - 4) Step 4 Thus, the factors of the polynomial 5b 2-18b - 8 are (5b + 2) and (b - 4).

8 (10) (5x + 2) (5x + 2) (5x - 2) (5x - 2) ID : ae-8-factorisation [8] Let's factorize 625x 4-200x = 625x 4-200x = (25x 2 ) 2 - (2 4 25) Since we know that (a - b) 2 = a 2-2ab + b 2 ] = (25x 2-4) 2 = {(5x) } 2 = {(5x + 2)(5x - 2)} 2...[Since we know that a 2 - b 2 = (a + b)(a - b)] = (5x + 2)(5x + 2)(5x - 2)(5x - 2) Thus, the factors of (625x 4-200x ) are (5x + 2), (5x + 2), (5x - 2) and (5x - 2).

### Class 8 Factorisation

ID : in-8-factorisation [1] Class 8 Factorisation For more such worksheets visit www.edugain.com Answer the questions (1) Find factors of following polynomial A) xy - 7y + 9x - 63 B) xy - 5y + 6x - 30

ID : ae-8-algebraic-identities [1] Grade 8 Algebraic Identities For more such worksheets visit www.edugain.com Answer t he quest ions (1) If, f ind the value of. (2) If 3(p 2 + q 2 + r 2 ) = (p + q + r)

### Class 10 Polynomials. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

ID : in-10-polynomials [1] Class 10 Polynomials For more such worksheets visit www.edugain.com Answer t he quest ions (1) If α and β are the zeros of quadratic polynomial x 2 + px - 2q, f ind the value

### Class 8 Multiplication of Polynomials

ID : in-8-multiplication-of-polynomials [1] Class 8 Multiplication of Polynomials For more such worksheets visit www.edugain.com Answer t he quest ions (1) If (2pq + 2p) ( -2pq + 2p + 2) = ( -4p 2 q 2

### Class 7 Symmetry. Answer the questions. For more such worksheets visit (1) Find the order of rotational symmetry in the given image.

ID : in-7-symmetry [1] Class 7 Symmetry For more such worksheets visit www.edugain.com Answer the questions (1) Find the order of rotational symmetry in the given image. (2) How many lines of symmetry

### Grade 7 Algebra-Expressions and Equations

ID : ae-7-algebra-expressions-and-equations [1] Grade 7 Algebra-Expressions and Equations For more such worksheets visit www.edugain.com Answer the questions (1) Find the sum of following polynomials:

### Grade 6 Integers. Answer t he quest ions. Fill in the blanks. For more such worksheets visit

ID : ae-6-integers [1] Grade 6 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Find the predecessor of each of the f ollowing integers: A) -98 = B) -63 = C) -8 = D) -3

### 1. A polynomial p(x) in one variable x is an algebraic expression in x of the form

POLYNOMIALS Important Points 1. A polynomial p(x) in one variable x is an algebraic expression in x of the form p(x) = a nx n +a n-1x n-1 + a 2x 2 +a 1x 1 +a 0x 0 where a 0, a 1, a 2 a n are constants

### Class 7 Integers. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks

ID : in-7-integers [1] Class 7 Integers For more such worksheets visit www.edugain.com Answer the questions (1) An integer is divided by 4 and gives a remainder of 3. The resulting quotient is divided

### Question: 1. Use suitable identities to find the following products:

CH-2 Polynomial Question: 1. Use suitable identities to find the following products: (i) (x + 4) (x + 10) Solution:- (x+4)(x+10) = x 2 +10x+4x+4 x 10 = x 2 +14x+40 (ii) (x + 8) (x 10) Solution: x 2-10x+8x-80

### Grade 9 Linear Equations in Two Variables

ID : cn-9-linear-equations-in-two-variables [1] Grade 9 Linear Equations in Two Variables For more such worksheets visit www.edugain.com Answer the questions (1) In the graph of the linear equation 4x

### Grade 7 Integers. Answer the questions. For more such worksheets visit

ID : ae-7-integers [1] Grade 7 Integers For more such worksheets visit www.edugain.com Answer the questions (1) A railway company makes a profit of Dhs 1570 on per ticket of business class while loses

### Grade 4 Conversion of Units

ID : ae-4-conversion-of-units [1] Grade 4 Conversion of Units For more such worksheets visit www.edugain.com Answer the questions (1) A water storage tank is filled with 94 l of water. On the first day

### 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

ID : ae-9-number-system [] Grade 9 Number System For more such worksheets visit www.edugain.com Answer t he quest ions () Write a multiple of -5-7 rational number? (2) Express the f ollowing numbers in

### Class 8 Full Year 8th Grade Review

ID : in-8-full-year-8th-grade-review [1] Class 8 Full Year 8th Grade Review For more such worksheets visit www.edugain.com Answer the questions (1) The given figure shows some fruits in a basket. Gauri

ID : ae-10-full-year-10th-grade-review [1] Grade 10 Full Year 10th Grade Review For more such worksheets visit www.edugain.com Answer the questions (1) The sum of the n consecutive natural even numbers

### Math 10 - Unit 5 Final Review - Polynomials

Class: Date: Math 10 - Unit 5 Final Review - Polynomials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Factor the binomial 44a + 99a 2. a. a(44 + 99a)

MTH 310-3 Abstract Algebra I and Number Theory S18 Homework 1/Solutions Graded Exercises Exercise 1. Below are parts of the addition table and parts of the multiplication table of a ring. Complete both

ID : ae-10-quadratic-equations [1] Grade 10 Quadratic Equations For more such worksheets visit www.edugain.com Answer t he quest ions (1) A two digit number is such that the product of its digits is 15.

ID : ww-0-arithmetic-progressions [] Grade 0 Arithmetic Progressions For more such worksheets visit www.edugain.com Answer t he quest ions () The nth term of an arithmetic progression is given by the equation

ID : us-0-arithmetic-progressions [] Grade 0 Arithmetic Progressions For more such worksheets visit www.edugain.com Answer t he quest ions () The sum of f irst 9 terms of an arithmetic progression is -234

### Class 6 Full Year 6th Grade Review

ID : in-6-full-year-6th-grade-review [1] Class 6 Full Year 6th Grade Review For more such worksheets visit www.edugain.com Answer the questions (1) Parallelogram ABCD is given below, what is the ratio

ID : ae-5-decimal-numbers [1] Grade 5 Decimal Numbers For more such worksheets visit www.edugain.com Answer the questions (1) Which number is 0.26 less than the largest 2-digit number? (2) What is the

### CHAPTER 2 BOOLEAN ALGEBRA

CHAPTER 2 BOOLEAN ALGEBRA This chapter in the book includes: Objectives Study Guide 2.1 Introduction 2.2 Basic Operations 2.3 Boolean Expressions and Truth Tables 2.4 Basic Theorems 2.5 Commutative, Associative,

ID : ae-10-quadratic-equations [1] Grade 10 Quadratic Equations For more such worksheets visit www.edugain.com Answer the questions (1) Solve quadratic equation (x 0 and x -1). (2) The age of a mother

### Grade 7 Triangle and its properties

ID : ae-7-triangle-and-its-properties [1] Grade 7 Triangle and its properties For more such worksheets visit www.edugain.com Answer t he quest ions (1) In triangle In ΔABC, D is a point on the side BC

### Grade 5 Geometry. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks

ID : cn-5-geometry [1] Grade 5 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) What is the common term for the perimeter of a circle? (2) What is the perimeter of an isosceles

ID : in-10-quadratic-equations [1] Class 10 Quadratic Equations For more such worksheets visit www.edugain.com Answer the questions (1) The sum of square of two positive numbers is 832. If square of the

### L Y Q S F C. Class 7 Symmetry. Answer t he quest ions. For more such worksheets visit

ID : in-7-symmetry [1] Class 7 Symmetry For more such worksheets visit www.edugain.com Answer t he quest ions (1) Find the order of rotational symmetry in f ollowing image. (2) How many lines of symmetry

### Grade 4 2nd three months in school

ID : ae-4-2nd-three-months-in-school [1] Grade 4 2nd three months in school For more such worksheets visit www.edugain.com Answer the questions (1) If 16 kg of corn is required to make food for 688 people,

### Graphing Square Roots - Class Work Graph the following equations by hand. State the domain and range of each using interval notation.

Graphing Square Roots - Class Work Graph the following equations by hand. State the domain and range of each using interval notation. 1. y = x + 2 2. f(x) = x 1. y = x +. g(x) = 2 x 1. y = x + 2 + 6. h(x)

### What is a constant? A Constant is a number representing a quantity or value that does not change.

Worksheet -: Algebraic Expressions What is a constant? A Constant is a number representing a quantity or value that does not change. What is a variable? A variable is a letter or symbol representing a

### Class 4 Fractions. Answer t he quest ions. For more such worksheets visit

ID : infractions [] Class Fractions For more such worksheets visit www.edugain.com Answer t he quest ions () Which mixed f raction is shown by the f igure given below? () If sum of both horizontal and

### Grade 7 Integers. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks

ID : ae-7-integers [1] Grade 7 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Subtract : A) 21644 f rom 22642 B) -4505 f rom -83570 C) 133 f rom 16220 D) -56723 f rom

### Grade 6 Integers. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks

ID : ww-6-integers [1] Grade 6 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Subtract : A) -8566 f rom 37583-73166 f rom 13448-62694 f rom 11073 57430 f rom -53545

### CM2104: Computational Mathematics General Maths: 2. Algebra - Factorisation

CM204: Computational Mathematics General Maths: 2. Algebra - Factorisation Prof. David Marshall School of Computer Science & Informatics Factorisation Factorisation is a way of simplifying algebraic expressions.

### Class 4 Conversion of Units

ID : in-4-conversion-of-units [1] Class 4 Conversion of Units For more such worksheets visit www.edugain.com Answer the questions (1) Convert the following: 17km 28hm 40dam 35m = m (2) 18 decigrams = grams

### 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

### Class 6 Geometry. Answer the questions. For more such worksheets visit (1) If AB and DE are parallel, find the value of ACB.

ID : in-6-geometry [1] Class 6 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) If AB and DE are parallel, find the value of ACB. (2) If AB and DE are parallel to each other,

### Chapter 5 Rational Expressions

Worksheet 4 (5.1 Chapter 5 Rational Expressions 5.1 Simplifying Rational Expressions Summary 1: Definitions and General Properties of Rational Numbers and Rational Expressions A rational number can be

### Polynomials. In many problems, it is useful to write polynomials as products. For example, when solving equations: Example:

Polynomials Monomials: 10, 5x, 3x 2, x 3, 4x 2 y 6, or 5xyz 2. A monomial is a product of quantities some of which are unknown. Polynomials: 10 + 5x 3x 2 + x 3, or 4x 2 y 6 + 5xyz 2. A polynomial is a

### Grade 10 Linear Equations in Two Variables

ID : ae-10-linear-equations-in-two-variables [1] Grade 10 Linear Equations in Two Variables For more such worksheets visit www.edugain.com Answer t he quest ions (1) 12 chairs and 10 tables cost Dhs4700

ID : ae--rational-numbers [1] Grade Rational Numbers For more such worksheets visit wwwedugaincom Answer t he quest ions (1) Find the dif f erence between the greatest and the least numbers of - 4-24 9

ID : gb-5-large-numbers [1] Grade 5 Large Numbers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Arrange the f ollowing numbers in Ascending Order: 34606246, 33371563, 23968628,

### CP Algebra 2 Unit 2-1: Factoring and Solving Quadratics WORKSHEET PACKET

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

### Algebraic Expressions

Algebraic Expressions 1. Expressions are formed from variables and constants. 2. Terms are added to form expressions. Terms themselves are formed as product of factors. 3. Expressions that contain exactly

### Graphing Square Roots - Class Work Graph the following equations by hand. State the domain and range of each using interval notation.

Graphing quare Roots - lass Work Graph the following equations by hand. tate the domain and range of each using interval notation. 1. y = x + 2 2. f x = x 1. y = x + 4. g x = 2 x 1 5. y = x + 2 + 4 6.

### Grade 6 Geometry. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

ID : ww-6-geometry [1] Grade 6 Geometry For more such worksheets visit www.edugain.com Answer t he quest ions (1) If AB and CD are parallel, f ind the value of angle x. Choose correct answer(s) f rom given

### Answers to Sample Exam Problems

Math Answers to Sample Exam Problems () Find the absolute value, reciprocal, opposite of a if a = 9; a = ; Absolute value: 9 = 9; = ; Reciprocal: 9 ; ; Opposite: 9; () Commutative law; Associative law;

### On a class of three-variable inequalities. Vo Quoc Ba Can

On a class of three-variable inequalities Vo Quoc Ba Can 1 Theem Let a, b, c be real numbers satisfying a + b + c = 1 By the AM - GM inequality, we have ab + bc + ca 1, therefe setting ab + bc + ca = 1

ID : sg-8-rational-numbers [1] Grade 8 Rational Numbers For more such worksheets visit wwwedugaincom Answer t he quest ions (1) Is 003 the multiplicative inverse of 33 1 3? Why or why not? (2) What is

ID : ae-4-logical-reasoning [1] Grade 4 Logical Reasoning For more such worksheets visit www.edugain.com Answer the questions (1) 9999 = 9000 + + 9. What is the missing number? (2) The table shows description

### Class 9 Linear Equations in Two Variables

ID : in-9-linear-equations-in-two-variables [1] Class 9 Linear Equations in Two Variables For more such worksheets visit www.edugain.com Answer the questions (1) A telecom operator charges Rs. 1.1 for

### Chapter 7: Exponents

Chapter : Exponents Algebra Chapter Notes Name: Algebra Homework: Chapter (Homework is listed by date assigned; homework is due the following class period) HW# Date In-Class Homework M / Review of Sections.-.

### ( ) Chapter 6 ( ) ( ) ( ) ( ) Exercise Set The greatest common factor is x + 3.

Chapter 6 Exercise Set 6.1 1. A prime number is an integer greater than 1 that has exactly two factors, itself and 1. 3. To factor an expression means to write the expression as the product of factors.

### Chapter 7: Exponents

Chapter 7: Exponents Algebra 1 Chapter 7 Notes Name: Algebra Homework: Chapter 7 (Homework is listed by date assigned; homework is due the following class period) HW# Date In-Class Homework Section 7.:

### Expanding brackets and factorising

CHAPTER 8 Epanding brackets and factorising 8 CHAPTER Epanding brackets and factorising 8.1 Epanding brackets There are three rows. Each row has n students. The number of students is 3 n 3n. Two students

### Class 7 Olympiad. Answer the questions. For more such worksheets visit

ID : in-7-olympiad [1] Class 7 Olympiad For more such worksheets visit www.edugain.com Answer the questions (1) When 24 is added to 40 % of a number, it gives the number itself. Find the number. (2) If

### Class 5 4th quarter in school

ID : in-5-4th-quarter-in-school [1] Class 5 4th quarter in school For more such worksheets visit www.edugain.com Answer the questions (1) For the last 4 days, Ram is spending the same amount every day.

### Class 6 Second quarter at school

ID : in6secondquarteratschool [] Class 6 Second quarter at school For more such worksheets visit wwwedugaincom Answer the questions () Find the value of the following : 7 () If the following figure represents

### A field trips costs \$800 for the charter bus plus \$10 per student for x students. The cost per student is represented by: 10x x

LEARNING STRATEGIES: Activate Prior Knowledge, Shared Reading, Think/Pair/Share, Note Taking, Group Presentation, Interactive Word Wall A field trips costs \$800 for the charter bus plus \$10 per student

### Class 7 Mensuration - Perimeter, Area, Volume

ID : U-92206-76-2397-Mensuration-Perimeter-Area-Volume [1] Class 7 Mensuration - Perimeter, Area, Volume For more such worksheets visit www.edugain.com Answer t he quest ions (1) The cost of f encing is

ID : in-10-quadratic-equations [1] Class 10 Quadratic Equations For more such worksheets visit www.edugain.com Answer t he quest ions (1) Had Sunil scored 8 more marks in his mathematics test out of 30

### Permutations and Polynomials Sarah Kitchen February 7, 2006

Permutations and Polynomials Sarah Kitchen February 7, 2006 Suppose you are given the equations x + y + z = a and 1 x + 1 y + 1 z = 1 a, and are asked to prove that one of x,y, and z is equal to a. We

### 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)

### IES Parque Lineal - 2º ESO

UNIT5. ALGEBRA Contenido 1. Algebraic expressions.... 1 Worksheet: algebraic expressions.... 2 2. Monomials.... 3 Worksheet: monomials.... 5 3. Polynomials... 6 Worksheet: polynomials... 9 4. Factorising....

### UNC Charlotte Super Competition Level 3 Test March 4, 2019 Test with Solutions for Sponsors

. Find the minimum value of the function f (x) x 2 + (A) 6 (B) 3 6 (C) 4 Solution. We have f (x) x 2 + + x 2 + (D) 3 4, which is equivalent to x 0. x 2 + (E) x 2 +, x R. x 2 + 2 (x 2 + ) 2. How many solutions

### 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:

### LESSON 7.1 FACTORING POLYNOMIALS I

LESSON 7.1 FACTORING POLYNOMIALS I LESSON 7.1 FACTORING POLYNOMIALS I 293 OVERVIEW Here s what you ll learn in this lesson: Greatest Common Factor a. Finding the greatest common factor (GCF) of a set of

### Class 4 Division. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

ID : in-4-division [1] Class 4 Division For more such worksheets visit www.edugain.com Answer t he quest ions (1) Division is a repeated f orm of which other mathematical operation? Choose correct answer(s)

### Grade 6 Decimals. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

ID : ae-6-decimals [1] Grade 6 Decimals For more such worksheets visit www.edugain.com Answer t he quest ions (1) What do you get when you divide 323.61 by 48.3? (2) The juice cart sells 192.65 liters

### Note: An algebraic expression is made of one or more terms. The terms in an algebraic expression are connected with either addition or subtraction.

.4 Combining Like Terms Term A term is a single number or variable, or it can be a product of a number (called its coefficient) and one or more variables. Examples of terms:, x, a, xy, 4 a bc, 5, xyz coefficient

### LOWELL WEEKLY JOURNAL

Y G y G Y 87 y Y 8 Y - \$ X ; ; y y q 8 y \$8 \$ \$ \$ G 8 q < 8 6 4 y 8 7 4 8 8 < < y 6 \$ q - - y G y G - Y y y 8 y y y Y Y 7-7- G - y y y ) y - y y y y - - y - y 87 7-7- G G < G y G y y 6 X y G y y y 87 G

### Expressions and Formulae

Topic by Topic Revision Part 1 Expressions and Formulae Attempt Section A Start with Surds and Indices Q1 (a) (c). If you can attempt these three questions successfully (without checking your notes or

### Basic Algebra. CAPS Mathematics

Basic Algebra CAPS Mathematics 1 Outcomes for this TOPIC In this TOPIC you will: Revise factorization. LESSON 1. Revise simplification of algebraic fractions. LESSON. Discuss when trinomials can be factorized.

### Class 4 Decimals. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

ID : in-4-decimals [1] Class 4 Decimals For more such worksheets visit www.edugain.com Answer t he quest ions (1) Write the number one Ten thousandths in decimal f orm (2) What do you get when you subtract

### (5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5).

ID : ww-9-olympiad [1] Grade 9 Olympiad For more such worksheets visit www.edugain.com Answer t he quest ions (1) If a cone and hemisphere stands on equal bases, and have the same height. Find the ratio

### AMC Lecture Notes. Justin Stevens. Cybermath Academy

AMC Lecture Notes Justin Stevens Cybermath Academy Contents 1 Systems of Equations 1 1 Systems of Equations 1.1 Substitution Example 1.1. Solve the system below for x and y: x y = 4, 2x + y = 29. Solution.

### Multivariable Calculus and Matrix Algebra-Summer 2017

Multivariable Calculus and Matrix Algebra-Summer 017 Homework 4 Solutions Note that the solutions below are for the latest version of the problems posted. For those of you who worked on an earlier version

### 8.6 Multiplication of Polynomials

8.6. Multiplication of Polynomials www.ck12.org 8.6 Multiplication of Polynomials Learning Objectives Multiply a polynomial by a monomial Multiply a polynomial by a binomial Solve problems using multiplication

### x 9 or x > 10 Name: Class: Date: 1 How many natural numbers are between 1.5 and 4.5 on the number line?

1 How many natural numbers are between 1.5 and 4.5 on the number line? 2 How many composite numbers are between 7 and 13 on the number line? 3 How many prime numbers are between 7 and 20 on the number

### CHAPTER 1. Review of Algebra

CHAPTER 1 Review of Algebra Much of the material in this chapter is revision from GCSE maths (although some of the exercises are harder). Some of it particularly the work on logarithms may be new if you

### Class 10 Real Numbers

ID : in-10-real-numbers [1] Class 10 Real Numbers For more such worksheets visit www.edugain.com Answer t he quest ions (1) The LCM of two numbers is 760 and their product is 6080. Find their HCF. (2)

### CHAPTER 3 BOOLEAN ALGEBRA

CHAPTER 3 BOOLEAN ALGEBRA (continued) This chapter in the book includes: Objectives Study Guide 3.1 Multiplying Out and Factoring Expressions 3.2 Exclusive-OR and Equivalence Operations 3.3 The Consensus

### Summer Prep Packet for students entering Algebra 2

Summer Prep Packet for students entering Algebra The following skills and concepts included in this packet are vital for your success in Algebra. The Mt. Hebron Math Department encourages all students

### The City School. Comprehensive Worksheet (2 nd Term) Mathematics Class 8. Branch/Campus:

The City School Comprehensive Worksheet (2 nd Term) 2017-2018 Mathematics Class 8 Index No: Branch/Campus: Maximum Marks: 100 Section: Date: Time Allowed:2 hours INSTRUCTIONS Write your index number, section,

ID : ww-8-full-year-8th-grade-review [1] Grade 8 Full Year 8th Grade Review For more such worksheets visit www.edugain.com Answer t he quest ions (1) Find the 6 rational numbers between -3 10 and -7 10.

### Multiplying Monomials

320 Chapter 5 Polynomials Eample 1 Multiplying Monomials Multiply the monomials. a. 13 2 y 7 215 3 y2 b. 1 3 4 y 3 21 2 6 yz 8 2 a. 13 2 y 7 215 3 y2 13 521 2 3 21y 7 y2 15 5 y 8 Group coefficients and

### Factorisation. Learn and Remember. Sol. Let the duration of each period be x. Period 8 9. Duration of period 45 x (min.)

246 MATHEMATICS-I Sol. Let the duration of each period be x. Period 8 9 Duration of period 45 x (min.) If the period increases then the duration of period decreases. So, it is a case of inverse proportion...

### Real Numbers. Real numbers are divided into two types, rational numbers and irrational numbers

Real Numbers Real numbers are divided into two types, rational numbers and irrational numbers I. Rational Numbers: Any number that can be expressed as the quotient of two integers. (fraction). Any number

ID : ww-5-multiplication [1] Grade 5 Multiplication For more such worksheets visit www.edugain.com Answer t he quest ions (1) Sharon is practicing to participate in an upcoming marathon. She runs 17 km

### SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-2) MATHEMATICS CLASS IX

SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-) MATHEMATICS CLASS IX Time: 3 to 3 1 hours Maximum Marks: 80 GENERAL INSTRUCTIONS: 1. All questions are compulsory.. The question paper is divided into four sections

### A polynomial expression is the addition or subtraction of many algebraic terms with positive integer powers.

LEAVING CERT Honours Maths notes on Algebra. A polynomial expression is the addition or subtraction of many algebraic terms with positive integer powers. The degree is the highest power of x. 3x 2 + 2x

### Algebra III and Trigonometry Summer Assignment

Algebra III and Trigonometry Summer Assignment Welcome to Algebra III and Trigonometry! This summer assignment is a review of the skills you learned in Algebra II. Please bring this assignment with you

### Class 7 Lines and Angles

ID : in-7-lines-and-angles [1] Class 7 Lines and Angles For more such worksheets visit www.edugain.com Answer the questions (1) ABCD is a quadrilateral whose diagonals intersect each other at point O such

### Exponents and Polynomials. (5) Page 459 #15 43 Second Column; Page 466 #6 30 Fourth Column

Algebra Name: Date: Period: # Exponents and Polynomials (1) Page 453 #22 59 Left (2) Page 453 #25 62 Right (3) Page 459 #5 29 Odd (4) Page 459 #14 42 First Column; Page 466 #3 27 First Column (5) Page

### ( ) y 2! 4. ( )( y! 2)

1. Dividing: 4x3! 8x 2 + 6x 2x 5.7 Division of Polynomials = 4x3 2x! 8x2 2x + 6x 2x = 2x2! 4 3. Dividing: 1x4 + 15x 3! 2x 2!5x 2 = 1x4!5x 2 + 15x3!5x 2! 2x2!5x 2 =!2x2! 3x + 4 5. Dividing: 8y5 + 1y 3!