Factoring Polynomials10-2 (page 565 – 571)

Distributing and Grouping

By: Julie and Shelby

Warm Up!

Review: GCF/GMF (Greatest Common Factor and Greatest Monomial Factor)

Find the GCF: Factor each Monomial:

1. 24, 48 3. 44sb2j

2. 16, 72 4. 24c5,

5. 26js4, 16j3, 8j2

Factoring Polynomials:Method 1: Distributing

• When factoring polynomials use the distributive property backwards

Ex: 12mn2 + 18m2n2

Step 1: Factor and find the GCF of the monomials

12mn2= 2 * 2 * 3 * m * n * n 18m2n2= 2 * 3 * 3 * m * m * n * n The GCF = 2 * 3 * m * n * n or 6mn2

• Step 2: Now rewrite problem so the GCF will be distributed by dividing it (6mn2) and putting it outside the parentheses and distributing it over whatever is left:

6mn2(2 – 3m)

• Step 3: Check by redistributing to make sure you come up with the original problem

• Example 2: 20abc + 15a2c – 5acRemember: Step One Factor

Step Two Distribute

Step Three Check

20abc = 15a2c =5ac =

Practice1.)12a – 48a2b 2.) 14r2t – 42t = __t(__ - 3)

Factoring Polynomials:Method 2: Grouping

• The other method of factoring polynomials is grouping, which uses the associative property. This method is used when factoring four or more polynomials.

Ex: 12ac + 21ad + 8bc + 14bd

Step 1: Apply the associative property (12ac + 21ad) + (8bc + 14 bd)

Step2: Find a common factor between each pair of terms. 12ac + 21ad would have a common factor of

3a. 8bc + 14bd would have a common factor of 2b.

Step 3: Factor the first two terms and the last two terms (12ac + 21ad) + (8bc + 14 bd) = 3a(4c + 7d) + 2b(4c + 7d)

Because 4c + 7d is a common factor and inside both parentheses, then it can be simplified further.

3a(4c + 7d) + 2b(4c + 7d) = (3a + 2b)(4c + 7d)

Step 4: Check with the FOIL method

F O I L(3a + 2b) (4c + 7d) = (3a)(4c) + (3a)(7d) + (2b)(4c) +=(2b)(7d)=

12ac 21ad 8bc 14bd

Note: If inside the parentheses are not the same, that is as simplified as it will get, but usually they will work out.

• Example 2: 20s + 12j = 4(5s + __) Work backwards to solve the

problem 20s/4 =12j/4 =

Example 3: (6x2 – 10xy) + (9x – 15y) = 2x(__) + 3(__)

*3x - 5y

Practice1.) 5a – 20 +ac – 4c 2.) 3c – 3 +ac – a

More PracticeExpress the Polynomials in

Factored Form1.) 9t2 + 36t 2.) 2mk + 7x + 7m + 2xk

3.) 2ax + 6xc + ba + 3bc 4.) 6mn + 15m2