factoring by grouping common core algebra 1 homework answers

Factoring by Common Factors & by Grouping

In these lessons, we will look at factoring by common factors and factoring of polynomials by grouping.

Related Pages More Factoring and Algebra Lessons Algebra Worksheets Algebra Games

The following diagram shows the steps to factor a polynomial with four terms using grouping. Scroll down the page for examples and solutions.

The following diagram shows the steps to factor a trinomial using grouping. Scroll down the page for examples and solutions.

Factoring By Common Factors

The first step in factorizing is to find and extract the GCF of all the terms.

Example: Factorize the following algebraic expressions: a) xyz – x 2 z b) 6a 2 b + 4bc

Solution: a) xyz – x 2 z = xz(y – x) b) 6a 2 b + 4bc = 2b(3a 2 + 2c)

Factoring Out The Greatest Common Factor Factoring is a technique that is useful when trying to solve polynomial equations algebraically. We begin by looking for the Greatest Common Factor (GCF) of a polynomial expression. The GCF is the largest monomial that divides (is a factor of) each term of of the polynomial. The following video shows an example of simple factoring or factoring by common factors. To find the GCF of a Polynomial

• Write each term in prime factored form
• Identify the factors common in all terms
• Factor out the GCF

Examples: Factor out the GCF

• 2x 4 - 16x 3
• 4x 2 y 3 + 20xy 2 + 12xy
• -2x 3 + 8x 2 - 4x
• -y 3 - 2y 2 + y - 7

Factoring Using the Great Common Factor, GCF - Example 1 Two examples of factoring out the greatest common factor to rewrite a polynomial expression.

Example: Factor out the GCF: a) 2x 3 y 8 + 6x 4 y 2 + 10x 5 y 10 b) 6a 10 b 8 + 3a 7 b 4 - 24a 5 b 6

Factoring Using the Great Common Factor, GCF - Example 2

Example: Factor out binomial expressions. a) 3x 2 (2x + 5y) + 7y 2 (2x + 5y) b) 5x 2 (x + 3y) - 15x 3 (x + 3y)

Factoring Polynomials with Common Factors This video provides examples of how to factor polynomials that require factoring out the GCF as the first step. Then other methods are used to completely factor the polynomial.

Example: Factor 4x 2 - 64 3x 2 + 3x - 36 2x 2 - 28x + 98

Factoring By Grouping

When an expression has an even number of terms and there are no common factors for all the terms, we may group the terms into pairs and find the common factor for each pair:

Example: Factorize the following expressions:

a) ax + ay + bx + by b) 2x + 8y – 3px –12py c) 3x – 3y + 4ay – 4ax

Solution: a) ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)

b) 2x + 8y – 3px –12py = 2(x + 4y) –3p(x + 4y) = (2 – 3p)(x + 4y)

c) 3x – 3y + 4ay – 4ax = 3(x – y) + 4a(y – x) = 3(x – y) – 4a(x – y) = (3 – 4a)( x – y)

How to Factor by Grouping? 3 complete examples of solving quadratic equations using factoring by grouping are shown.

• Factor x(x + 1) - 5(x + 1)
• Solve 2x 2 + 5x + 2 = 0
• Solve 7x 2 + 16x + 4 = 0
• Solve 6x 2 - 17x + 12 = 0

Factoring by Grouping - Ex 1

Example: Factor: a) 2x 2 + 7x 2 + 2x + 7 b) 10x 2 + 2xy + 15xy + 3y 2

Factoring By Grouping - Ex 2

Example: Factor: 12u 2 + 15uv + 24uv 2 + 30v 3

Factoring Trinomials: Factor by Grouping - ex 1

Example: Factor 12x 2 + 34x + 10

Factoring Trinomials: Factor by Grouping - ex 2

Example: Factor 6x 2 + 15x - 21

Factoring by grouping - Prime Factorization

Example: 12a 3 - 9a 2 b - 8ab 2 + 6b 3

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Factoring by Grouping

We can sometimes factor a difficult-looking polynomial through the creative use of the distributive property . This is called factoring by grouping.

Factoring by grouping in action

The polynomial 2 ⁢ x ⁢ y - 6 ⁢ x ⁢ z + 3 ⁢ y - 9 ⁢ z looks a little intimidating, but the coefficients have a proportional relationship we can exploit. The 2 and -6 are both divisible by 2, and both terms have an x . That means we can use the distributive property to factor out 2x from both sides of the first two terms:

2 x y - 6 x z = ⁢ 2 ⁢ x ( y - 3 ⁢ z )

Similarly, we can factor out a 3 from the other two terms:

3 ⁢ y - 9 ⁢ z = 3 ⁢ ( y - 3 ⁢ z )

The quantity y - 3 ⁢ z appears in both factored terms, allowing us to use the distributive property one more time to get a simplified answer of:

2 ⁢ x ⁢ ( y - 3 ⁢ z ) + 3 ⁢ ( y - 3 ⁢ z ) = ( 2 ⁢ x + 3 ) ⁢ ( y - 3 ⁢ z )

Factoring by grouping practice question

Factor x 2 + x ⁢ y + 3 ⁢ x + 3 ⁢ y

We can begin by grouping the terms as follows:

( x 2 + 3 ⁢ x ) ⁢ ( x ⁢ y + 3 ⁢ y )

Both terms have x + 3 as a factor, so we can use the distributive property to simplify

x ⁢ ( x + 3 ) + y ⁢ ( x + 3 )

into a final answer of

( x + y ) ⁢ ( x + 3 )

Topics related to the Factoring by Grouping

Advanced Factoring

Solving Quadratic Equations using Factoring

Graphing Quadratic Equations Using Factoring

Flashcards covering the Factoring by Grouping

Algebra 1 Flashcards

College Algebra Flashcards

Practice tests covering the Factoring by Grouping

Algebra 1 Diagnostic Tests

College Algebra Diagnostic Tests

Get help with factoring by grouping

Factoring by grouping is seldom the only way to factor a polynomial, but it's generally the easiest, fastest method when available. If your student isn't taking full advantage of it, they may not have enough time to complete exams or spend longer than needed on homework. Luckily, an experienced mathematics tutor could provide practice problems until factoring by grouping feels like second nature. Reach out to the Educational Directors at Varsity Tutors today to learn more.

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Factoring in Algebra: Factoring by Grouping

Factoring in Algebra can be accomplished in many different ways. When it comes to polynomials, each situation is different based on the make-up of the polynomial. In our last lesson, we learned how to factor by using the greatest common factor.

However, some polynomials have no greatest common factor other than 1. Therefore, we would need to choose another method for factoring.

In this case, we would look to see if the polynomial has a couple of terms with a common factor. If so, we can group them together and factor separately.

Take a look at the following example:

Example 1: Factoring by Grouping

3x 2 - 3 + x 2 y - y

There are 4 terms in the polynomial. However, there are no common factors within the 4 terms.

Do you see two terms that have a common factor that could be grouped together?

I know that factoring can be confusing, but think of factoring as rewriting the problem using the distributive property. You want to continue factoring a polynomial until no common factors exist.

Let's look at another example.

Example 2: Factoring by Grouping

Hopefully you now better understand how to factor polynomials using the grouping method. If you cannot factor by using grouping, then you may have a trinomial that can be factored using a different method.

• Polynomials
• Factoring by Grouping

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Factor By Grouping Worksheet and Key

Students will practice how to factor by grouping . This sheet has model problems worked out, step by step. 25 scaffolded questions that start out relatively easy and end with some real challenges.

Example Questions

Directions : Factor Completely .

Other Details

This is a 4 part worksheet:

• Part I Model Problems
• Part II Practice
• Part III Challenge Problems
• Part IV Answer Key
• Factoring by Grouping
• Methods of Factoring - different methods of factoring

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Common Core Algebra 1, Unit 9: Factoring

To begin Unit 9 in the Common Core Algebra I series, scholars view a video presentation on determining the greatest common factor for algebraic expressions. They see how to use factoring and the zero product property to solve polynomial equations. Another lesson focuses on factoring second-degree trinomials. Viewers also learn about the magic X method to keep track of the constant factors. The third lesson shows a technique to factor trinomials when the leading coefficient is not one. The series continues with pupils viewing a video presentation that shows how to combine all the factoring techniques from Unit 9 to factor in more complex polynomials. The unit review asks pupils to work through 16 problems to review factoring. The problems consist of straight factoring polynomial expressions, solving equations by factoring, and applying factoring to real-world problems.

Common Core

Greatest Common Factor

Practice Packet (.pdf)

Practice Solutions (.pdf)

Corrective Assignment (.pdf)

Greatest Common Factor (.mp4)

Factor Trinomials

Factor Trinomials (.mp4)

Factor Trinomials by Grouping

Multi-Step Factoring

Multi-Step Factoring (.mp4)

Unit 9 Review: Factoring

Unit 9 Review: Factoring (.html)

• $ 0.00 0 items

Unit 6 – Quadratic Functions and Their Algebra

Quadratic Function Review

LESSON/HOMEWORK

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

Factoring Trinomials

Complete Factoring

Factoring by Grouping

The Zero Product Law

Quadratic Inequalities in One Variable

Completing the Square and Shifting Parabolas

Modeling with Quadratic Functions

Equations of Circles

The Locus Definition of a Parabola

Unit Review

Unit 6 Review – Quadratic Functions

UNIT REVIEW

EDITABLE REVIEW

Unit 6 Assessment Form A

EDITABLE ASSESSMENT

Unit 6 Assessment Form B

Unit 6 Assessment Form C

Unit 6 Assessment Form D

Unit 6 Exit Tickets

Unit 6 – Mid-Unit Quiz (Through Lesson #6) – Form A

Unit 6 – Mid-Unit Quiz (Through Lesson #6) – Form B

Unit 6 – Mid-Unit Quiz (Through Lesson #6) – Form C

Unit 6 – Mid-Unit Quiz (Through Lesson #6) – Form D

U06.AO.01 – Lesson 5.4 – Factoring Trinomials Using the AC Method

EDITABLE RESOURCE

U06.AO.02 – Lesson 5.5 – Using Structure to Factor

U06.AO.03 – Lesson 9.5 – The Vertex Form of a Parabola

U06.AO.04 – Lesson 12 – More Work with the Directrix and Focus

U06.AO.05 – Parabola Practice

U06.AO.06 – Factoring Practice

U06.AO.07 – Quadratic Systems Practice

U06.AO.08 – Quadratic Inequalities in One Variable Practice

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7.1 Greatest Common Factor and Factor by Grouping

Learning objectives.

By the end of this section, you will be able to:

• Find the greatest common factor of two or more expressions
• Factor the greatest common factor from a polynomial
• Factor by grouping

Be Prepared 7.1

Before you get started, take this readiness quiz.

Factor 56 into primes. If you missed this problem, review Example 1.7 .

Be Prepared 7.2

Find the least common multiple of 18 and 24. If you missed this problem, review Example 1.10 .

Be Prepared 7.3

Simplify −3 ( 6 a + 11 ) −3 ( 6 a + 11 ) . If you missed this problem, review Example 1.135 .

Find the Greatest Common Factor of Two or More Expressions

Earlier we multiplied factors together to get a product. Now, we will be reversing this process; we will start with a product and then break it down into its factors. Splitting a product into factors is called factoring .

We have learned how to factor numbers to find the least common multiple (LCM) of two or more numbers. Now we will factor expressions and find the greatest common factor of two or more expressions. The method we use is similar to what we used to find the LCM.

Greatest Common Factor

The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.

First we’ll find the GCF of two numbers.

Example 7.1

How to find the greatest common factor of two or more expressions.

Find the GCF of 54 and 36.

Notice that, because the GCF is a factor of both numbers, 54 and 36 can be written as multiples of 18.

Find the GCF of 48 and 80.

Find the GCF of 18 and 40.

We summarize the steps we use to find the GCF below.

Find the Greatest Common Factor (GCF) of two expressions.

• Step 1. Factor each coefficient into primes. Write all variables with exponents in expanded form.
• Step 2. List all factors—matching common factors in a column. In each column, circle the common factors.
• Step 3. Bring down the common factors that all expressions share.
• Step 4. Multiply the factors.

In the first example, the GCF was a constant. In the next two examples, we will get variables in the greatest common factor.

Example 7.2

Find the greatest common factor of 27 x 3 and 18 x 4 27 x 3 and 18 x 4 .

Find the GCF: 12 x 2 , 18 x 3 12 x 2 , 18 x 3 .

Find the GCF: 16 y 2 , 24 y 3 16 y 2 , 24 y 3 .

Example 7.3

Find the GCF of 4 x 2 y , 6 x y 3 4 x 2 y , 6 x y 3 .

Find the GCF: 6 a b 4 , 8 a 2 b 6 a b 4 , 8 a 2 b .

Find the GCF: 9 m 5 n 2 , 12 m 3 n 9 m 5 n 2 , 12 m 3 n .

Example 7.4

Find the GCF of: 21 x 3 , 9 x 2 , 15 x 21 x 3 , 9 x 2 , 15 x .

Find the greatest common factor: 25 m 4 , 35 m 3 , 20 m 2 25 m 4 , 35 m 3 , 20 m 2 .

Find the greatest common factor: 14 x 3 , 70 x 2 , 105 x 14 x 3 , 70 x 2 , 105 x .

Factor the Greatest Common Factor from a Polynomial

Just like in arithmetic, where it is sometimes useful to represent a number in factored form (for example, 12 as 2 · 6 or 3 · 4 ) , 2 · 6 or 3 · 4 ) , in algebra, it can be useful to represent a polynomial in factored form. One way to do this is by finding the GCF of all the terms. Remember, we multiply a polynomial by a monomial as follows:

Now we will start with a product, like 2 x + 14 2 x + 14 , and end with its factors, 2 ( x + 7 ) 2 ( x + 7 ) . To do this we apply the Distributive Property “in reverse.”

We state the Distributive Property here just as you saw it in earlier chapters and “in reverse.”

Distributive Property

If a , b , c a , b , c are real numbers, then

The form on the left is used to multiply. The form on the right is used to factor.

So how do you use the Distributive Property to factor a polynomial? You just find the GCF of all the terms and write the polynomial as a product!

Example 7.5

How to factor the greatest common factor from a polynomial.

Factor: 4 x + 12 4 x + 12 .

Factor: 6 a + 24 6 a + 24 .

Try It 7.10

Factor: 2 b + 14 2 b + 14 .

Factor the greatest common factor from a polynomial.

• Step 1. Find the GCF of all the terms of the polynomial.
• Step 2. Rewrite each term as a product using the GCF.
• Step 3. Use the “reverse” Distributive Property to factor the expression.
• Step 4. Check by multiplying the factors.

Factor as a Noun and a Verb

We use “factor” as both a noun and a verb.

Example 7.6

Factor: 5 a + 5 5 a + 5 .

Try It 7.11

Factor: 14 x + 14 14 x + 14 .

Try It 7.12

Factor: 12 p + 12 12 p + 12 .

The expressions in the next example have several factors in common. Remember to write the GCF as the product of all the common factors.

Example 7.7

Factor: 12 x − 60 12 x − 60 .

Try It 7.13

Factor: 18 u − 36 18 u − 36 .

Try It 7.14

Factor: 30 y − 60 30 y − 60 .

Now we’ll factor the greatest common factor from a trinomial. We start by finding the GCF of all three terms.

Example 7.8

Factor: 4 y 2 + 24 y + 28 4 y 2 + 24 y + 28 .

We start by finding the GCF of all three terms.

Try It 7.15

Factor: 5 x 2 − 25 x + 15 5 x 2 − 25 x + 15 .

Try It 7.16

Factor: 3 y 2 − 12 y + 27 3 y 2 − 12 y + 27 .

Example 7.9

Factor: 5 x 3 − 25 x 2 5 x 3 − 25 x 2 .

Try It 7.17

Factor: 2 x 3 + 12 x 2 2 x 3 + 12 x 2 .

Try It 7.18

Factor: 6 y 3 − 15 y 2 6 y 3 − 15 y 2 .

Example 7.10

Factor: 21 x 3 − 9 x 2 + 15 x 21 x 3 − 9 x 2 + 15 x .

In a previous example we found the GCF of 21 x 3 , 9 x 2 , 15 x 21 x 3 , 9 x 2 , 15 x to be 3 x 3 x .

Try It 7.19

Factor: 20 x 3 − 10 x 2 + 14 x 20 x 3 − 10 x 2 + 14 x .

Try It 7.20

Factor: 24 y 3 − 12 y 2 − 20 y 24 y 3 − 12 y 2 − 20 y .

Example 7.11

Factor: 8 m 3 − 12 m 2 n + 20 m n 2 8 m 3 − 12 m 2 n + 20 m n 2 .

Try It 7.21

Factor: 9 x y 2 + 6 x 2 y 2 + 21 y 3 9 x y 2 + 6 x 2 y 2 + 21 y 3 .

Try It 7.22

Factor: 3 p 3 − 6 p 2 q + 9 p q 3 3 p 3 − 6 p 2 q + 9 p q 3 .

When the leading coefficient is negative, we factor the negative out as part of the GCF.

Example 7.12

Factor: −8 y − 24 −8 y − 24 .

When the leading coefficient is negative, the GCF will be negative.

Try It 7.23

Factor: −16 z − 64 −16 z − 64 .

Try It 7.24

Factor: −9 y − 27 −9 y − 27 .

Example 7.13

Factor: −6 a 2 + 36 a −6 a 2 + 36 a .

The leading coefficient is negative, so the GCF will be negative?

Try It 7.25

Factor: −4 b 2 + 16 b −4 b 2 + 16 b .

Try It 7.26

Factor: −7 a 2 + 21 a −7 a 2 + 21 a .

Example 7.14

Factor: 5 q ( q + 7 ) − 6 ( q + 7 ) 5 q ( q + 7 ) − 6 ( q + 7 ) .

The GCF is the binomial q + 7 q + 7 .

Try It 7.27

Factor: 4 m ( m + 3 ) − 7 ( m + 3 ) 4 m ( m + 3 ) − 7 ( m + 3 ) .

Try It 7.28

Factor: 8 n ( n − 4 ) + 5 ( n − 4 ) 8 n ( n − 4 ) + 5 ( n − 4 ) .

Factor by Grouping

When there is no common factor of all the terms of a polynomial, look for a common factor in just some of the terms. When there are four terms, a good way to start is by separating the polynomial into two parts with two terms in each part. Then look for the GCF in each part. If the polynomial can be factored, you will find a common factor emerges from both parts.

(Not all polynomials can be factored. Just like some numbers are prime, some polynomials are prime.)

Example 7.15

How to factor by grouping.

Factor: x y + 3 y + 2 x + 6 x y + 3 y + 2 x + 6 .

Try It 7.29

Factor: x y + 8 y + 3 x + 24 x y + 8 y + 3 x + 24 .

Try It 7.30

Factor: a b + 7 b + 8 a + 56 a b + 7 b + 8 a + 56 .

Factor by grouping.

• Step 1. Group terms with common factors.
• Step 2. Factor out the common factor in each group.
• Step 3. Factor the common factor from the expression.

Example 7.16

Factor: x 2 + 3 x − 2 x − 6 x 2 + 3 x − 2 x − 6 .

There is no GCF in all four terms. x 2 + 3 x −2 x − 6 Separate into two parts. x 2 + 3 x ⎵ −2 x − 6 ⎵ Factor the GCF from both parts. Be careful with the signs when factoring the GCF from the last two terms. x ( x + 3 ) − 2 ( x + 3 ) ( x + 3 ) ( x − 2 ) Check on your own by multiplying. There is no GCF in all four terms. x 2 + 3 x −2 x − 6 Separate into two parts. x 2 + 3 x ⎵ −2 x − 6 ⎵ Factor the GCF from both parts. Be careful with the signs when factoring the GCF from the last two terms. x ( x + 3 ) − 2 ( x + 3 ) ( x + 3 ) ( x − 2 ) Check on your own by multiplying.

Try It 7.31

Factor: x 2 + 2 x − 5 x − 10 x 2 + 2 x − 5 x − 10 .

Try It 7.32

Factor: y 2 + 4 y − 7 y − 28 y 2 + 4 y − 7 y − 28 .

Access these online resources for additional instruction and practice with greatest common factors (GFCs) and factoring by grouping.

• Greatest Common Factor (GCF)
• Factoring Out the GCF of a Binomial
• Greatest Common Factor (GCF) of Polynomials

Section 7.1 Exercises

Practice makes perfect.

In the following exercises, find the greatest common factor.

3 x , 10 x 2 3 x , 10 x 2

21 b 2 , 14 b 21 b 2 , 14 b

8 w 2 , 24 w 3 8 w 2 , 24 w 3

30 x 2 , 18 x 3 30 x 2 , 18 x 3

10 p 3 q , 12 p q 2 10 p 3 q , 12 p q 2

8 a 2 b 3 , 10 a b 2 8 a 2 b 3 , 10 a b 2

12 m 2 n 3 , 30 m 5 n 3 12 m 2 n 3 , 30 m 5 n 3

28 x 2 y 4 , 42 x 4 y 4 28 x 2 y 4 , 42 x 4 y 4

10 a 3 , 12 a 2 , 14 a 10 a 3 , 12 a 2 , 14 a

20 y 3 , 28 y 2 , 40 y 20 y 3 , 28 y 2 , 40 y

35 x 3 , 10 x 4 , 5 x 5 35 x 3 , 10 x 4 , 5 x 5

27 p 2 , 45 p 3 , 9 p 4 27 p 2 , 45 p 3 , 9 p 4

In the following exercises, factor the greatest common factor from each polynomial.

4 x + 20 4 x + 20

8 y + 16 8 y + 16

6 m + 9 6 m + 9

14 p + 35 14 p + 35

9 q + 9 9 q + 9

7 r + 7 7 r + 7

8 m − 8 8 m − 8

4 n − 4 4 n − 4

9 n − 63 9 n − 63

45 b − 18 45 b − 18

3 x 2 + 6 x − 9 3 x 2 + 6 x − 9

4 y 2 + 8 y − 4 4 y 2 + 8 y − 4

8 p 2 + 4 p + 2 8 p 2 + 4 p + 2

10 q 2 + 14 q + 20 10 q 2 + 14 q + 20

8 y 3 + 16 y 2 8 y 3 + 16 y 2

12 x 3 − 10 x 12 x 3 − 10 x

5 x 3 − 15 x 2 + 20 x 5 x 3 − 15 x 2 + 20 x

8 m 2 − 40 m + 16 8 m 2 − 40 m + 16

12 x y 2 + 18 x 2 y 2 − 30 y 3 12 x y 2 + 18 x 2 y 2 − 30 y 3

21 p q 2 + 35 p 2 q 2 − 28 q 3 21 p q 2 + 35 p 2 q 2 − 28 q 3

−2 x − 4 −2 x − 4

−3 b + 12 −3 b + 12

5 x ( x + 1 ) + 3 ( x + 1 ) 5 x ( x + 1 ) + 3 ( x + 1 )

2 x ( x − 1 ) + 9 ( x − 1 ) 2 x ( x − 1 ) + 9 ( x − 1 )

3 b ( b − 2 ) − 13 ( b − 2 ) 3 b ( b − 2 ) − 13 ( b − 2 )

6 m ( m − 5 ) − 7 ( m − 5 ) 6 m ( m − 5 ) − 7 ( m − 5 )

In the following exercises, factor by grouping.

x y + 2 y + 3 x + 6 x y + 2 y + 3 x + 6

m n + 4 n + 6 m + 24 m n + 4 n + 6 m + 24

u v − 9 u + 2 v − 18 u v − 9 u + 2 v − 18

p q − 10 p + 8 q − 80 p q − 10 p + 8 q − 80

b 2 + 5 b − 4 b − 20 b 2 + 5 b − 4 b − 20

m 2 + 6 m − 12 m − 72 m 2 + 6 m − 12 m − 72

p 2 + 4 p − 9 p − 36 p 2 + 4 p − 9 p − 36

x 2 + 5 x − 3 x − 15 x 2 + 5 x − 3 x − 15

Mixed Practice

In the following exercises, factor.

−20 x − 10 −20 x − 10

5 x 3 − x 2 + x 5 x 3 − x 2 + x

3 x 3 − 7 x 2 + 6 x − 14 3 x 3 − 7 x 2 + 6 x − 14

x 3 + x 2 − x − 1 x 3 + x 2 − x − 1

x 2 + x y + 5 x + 5 y x 2 + x y + 5 x + 5 y

5 x 3 + 3 x 2 − 5 x − 3 5 x 3 + 3 x 2 − 5 x − 3

Everyday Math

Area of a rectangle The area of a rectangle with length 6 less than the width is given by the expression w 2 − 6 w w 2 − 6 w , where w = w = width. Factor the greatest common factor from the polynomial.

Height of a baseball The height of a baseball t seconds after it is hit is given by the expression −16 t 2 + 80 t + 4 −16 t 2 + 80 t + 4 . Factor the greatest common factor from the polynomial.

Writing Exercises

The greatest common factor of 36 and 60 is 12. Explain what this means.

What is the GCF of y 4 , y 5 , and y 10 y 4 , y 5 , and y 10 ? Write a general rule that tells you how to find the GCF of y a , y b , and y c y a , y b , and y c .

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ If most of your checks were:

…confidently. Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific!

…with some help. This must be addressed quickly as topics you do not master become potholes in your road to success. Math is sequential—every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Whom can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no - I don’t get it! This is critical and you must not ignore it. You need to get help immediately or you will quickly be overwhelmed. See your instructor as soon as possible to discuss your situation. Together you can come up with a plan to get you the help you need.

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Access for free at https://openstax.org/books/elementary-algebra-2e/pages/1-introduction

• Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis
• Publisher/website: OpenStax
• Book title: Elementary Algebra 2e
• Publication date: Apr 22, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/elementary-algebra-2e/pages/1-introduction
• Section URL: https://openstax.org/books/elementary-algebra-2e/pages/7-1-greatest-common-factor-and-factor-by-grouping

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