Wednesday, October 16, 2002

Factoring the GCF from Polynomials

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.

Wednesday, October 16, 2002

Example:

14x2y = 2 7 x x y

Wednesday, October 16, 2002

Steps for Factoring the GCF From Polynomials

1. Write down the problem.

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.

Wednesday, October 16, 2002

Steps for Factoring the GCF From Polynomials

3. “Pair up” all factors that occur in each term and circle them.

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.

Wednesday, October 16, 2002

Example

Step 1

Step 2

3x3 + 6x2y – 15xy2

3x3 = 3 x x x6x2y = 2 3 x x y15xy2 = 3 5 x y y

Wednesday, October 16, 2002

Example

Step 3

Example

Step 3

Step 4

3x3 = 3 x x x6x2y = 2 3 x x y15xy2 = 3 5 x y y

3x (x2 + 2xy – 5y2)

Wednesday, October 16, 2002

Examples

We will do these together on the board.

A. 12a2b + 90a2b2c

B. 32m2n3 – 8m2n + 56m3n2

Wednesday, October 16, 2002

Try these yourself.

1. 15x2 – 20xy

2. 3x2 + 15x

3. 20abc + 15a2c – 5ac