1. Wednesday, October 16, 2002 Factoring the GCF from Polynomials

2. Wednesday, October 16, 2002 Review Algebraic Factorization is the writing of an expression as the product of prime numbers and variables with no variables having an exponent greater than one.

3. Wednesday, October 16, 2002 Example: 14x 2 y = 2 7 x x y

4. Wednesday, October 16, 2002 Steps for Factoring the GCF From Polynomials 1.Write down the problem.

5. Wednesday, October 16, 2002 Steps for Factoring the GCF From Polynomials 2.Write each term on a separate line and then write the algebraic factorization of each term.

6. Wednesday, October 16, 2002 Steps for Factoring the GCF From Polynomials 3.Pair up all factors that occur in each term and circle them.

7. Wednesday, October 16, 2002 Steps for Factoring the GCF From Polynomials 4.Multiply what is circled. This is the GCF. When writing the answer, put it outside parenthesis. The left- overs for each term should be multiplied and put inside parenthesis.

8. Wednesday, October 16, 2002 Example Step 1 Step 2 3x 3 + 6x 2 y – 15xy 2 3x 3 = 3 x x x 6x 2 y= 2 3 x x y 15xy 2 = 3 5 x y y

9. Wednesday, October 16, 2002 Example Step 3 Example Step 3 Step 4 3x 3 = 3 x x x 6x 2 y= 2 3 x x y 15xy 2 = 3 5 x y y 3x (x 2 + 2xy – 5y 2 )

10. Wednesday, October 16, 2002 Examples We will do these together on the board. A.12a 2 b + 90a 2 b 2 c B.32m 2 n 3 – 8m 2 n + 56m 3 n 2

11. Wednesday, October 16, 2002 Try these yourself. 1.15x 2 – 20xy 2.3x 2 + 15x 3.20abc + 15a 2 c – 5ac