Holt Algebra 1

8-2 Factoring by GCF8-2 Factoring by GCF

Holt Algebra 1

Warm Up

Lesson Presentation

Lesson Quiz

Section 8-2 1

Holt Algebra 1

8-2 Factoring by GCF

Bell Quiz 8-2

1. 2(w + 1)

2. 3x(x2 – 4)

Simplify.

Find the GCF of each pair of monomials.

3. 4h2 and 6h

4. 13p and 26p5

10 pts

possible

2 pts

2 pts

3 pts

3 pts

Section 8-2 2

Holt Algebra 1

8-2 Factoring by GCF

Questions on 0-9/8-1

Section 8-2 3

Holt Algebra 1

8-2 Factoring by GCF

Factor polynomials by using the greatest common factor.

Objective

Section 8-2 4

Holt Algebra 1

8-2 Factoring by GCF

Recall that the Distributive Property states that ab + ac =a(b + c). The Distributive Property allows you to “factor” out the GCF of the terms in

a polynomial to write a factored form of the polynomial.

Section 8-2 5

Holt Algebra 1

8-2 Factoring by GCF

Example 1: Factoring by Using the GCF

Factor each polynomial. Check your answer.

A: 2x2 – 4

B: 8x3 – 4x2 – 16x

C: –14x – 12x2

D: 3x3 + 2x2 – 10

Section 8-2 6

Holt Algebra 1

8-2 Factoring by GCF

When you factor out –1 as the first step, be sure to include it in all the other steps as well.

Caution!

Section 8-2 7

Holt Algebra 1

8-2 Factoring by GCF

Check It Out! Example 1Factor each polynomial. Check your answer.

a: 5b + 9b3

b: 9d2 – 82

c: –18y3 – 7y2

d: 8x4 + 4x3 – 2x2

Section 8-2 8

Holt Algebra 1

8-2 Factoring by GCF

Example 2: Science Application

SKIPSKIPSKIPSKIP

Section 8-2 9

Holt Algebra 1

8-2 Factoring by GCF

Sometimes the GCF of terms is a binomial. This GCF is called a common binomial factor. You factor out a common binomial factor the same way you factor out a monomial factor.

Section 8-2 10

Holt Algebra 1

8-2 Factoring by GCF

Example 3: Factoring Out a Common Binomial Factor

Factor each expression.

A. 5(x + 2) + 3x(x + 2)

B. –2b(b2 + 1)+ (b2 + 1)

Section 8-2 11

Holt Algebra 1

8-2 Factoring by GCF

Check It Out! Example 3

Factor each expression.

a. 4s(s + 6) – 5(s + 6)

b. 7x(2x + 3) + (2x + 3)

Section 8-2 12

Holt Algebra 1

8-2 Factoring by GCF

You may be able to factor a polynomial by grouping. When a polynomial has four terms, you can make two groups and factor out the GCF from each group.

Section 8-2 13

Holt Algebra 1

8-2 Factoring by GCF

Example 4: Factoring by Grouping

Factor each polynomial by grouping. Check your answer.

A: 6h4 – 4h3 + 12h – 8 B: 9x3 + 18x2 + x + 2 Add to packet notes

Section 8-2 14

Holt Algebra 1

8-2 Factoring by GCF

�Section 8Section 8Section 8Section 8----2 (page 535) 2 (page 535) 2 (page 535) 2 (page 535) 1, 2, 4, 5, 7, 8, 10, 11, 13, 1, 2, 4, 5, 7, 8, 10, 11, 13, 1, 2, 4, 5, 7, 8, 10, 11, 13, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 14, 16, 17, 19, 20, 22, 23, 14, 16, 17, 19, 20, 22, 23, 14, 16, 17, 19, 20, 22, 23, 25252525----29, 34, 37, 38, 39, 43, 29, 34, 37, 38, 39, 43, 29, 34, 37, 38, 39, 43, 29, 34, 37, 38, 39, 43, 44, 45, 50, 53, 54, 5944, 45, 50, 53, 54, 5944, 45, 50, 53, 54, 5944, 45, 50, 53, 54, 59----62626262

Section 8-2 15