1. Factoring Polynomials 10-2 (page 565 – 571) Distributing and Grouping
By: Julie and Shelby

2. Warm Up! Find the GCF: Factor each Monomial: 24, 48 3. 44sb2j
Review: GCF/GMF (Greatest Common Factor and Greatest Monomial Factor)
Find the GCF: Factor each Monomial:
24, sb2j
16, c5,
5. 26js4, 16j3, 8j2

3. 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

4. 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 – 5ac
Remember: Step One Factor
Step Two Distribute
Step Three Check
20abc =
15a2c =
5ac =

5. Practice
1.)12a – 48a2b ) 14r2t – 42t = __t(__ - 3)

6. 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)

7. 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)

8. Step 4: Check with the FOIL method
(3a + 2b) (4c + 7d) = (3a)(4c) + (3a)(7d) + (2b)(4c) +=(2b)(7d)=
12ac ad bc bd
Note: If inside the parentheses are not the same, that is as simplified as it will get, but usually they will work out.

9. 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

10. Practice
1.) 5a – 20 +ac – 4c 2.) 3c – 3 +ac – a

11. More Practice Express the Polynomials in Factored Form
1.) 9t2 + 36t ) 2mk + 7x + 7m + 2xk
3.) 2ax + 6xc + ba + 3bc 4.) 6mn + 15m2