Factoring the GCF from Polynomials

1. Factoring the GCF from Polynomials

2. 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. Example: • 14x2y = 2  7  x  x  y

4. Steps for Factoring the GCF From Polynomials • Write down the problem.

5. Steps for Factoring the GCF From Polynomials • Write each term on a separate line and then write the algebraic factorization of each term.

6. Steps for Factoring the GCF From Polynomials • “Pair up” all factors that occur in each term and circle them.

7. Steps for Factoring the GCF From Polynomials • 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. Step 1 Step 2 3x3 + 6x2y – 15xy2 3x3 = 3  x  x  x 6x2y = 2  3  x  x  y 15xy2 = 3  5  x  y  y Example

9. Step 3 Example Example Step 3 Step 4 3x3 = 3  x  x  x 6x2y = 2  3  x  x  y 15xy2 = 3  5  x  y  y 3x (x2 + 2xy – 5y2)

10. Examples • We will do these together on the board. • 12a2b + 90a2b2c • 32m2n3 – 8m2n + 56m3n2

11. Try these yourself. • 15x2 – 20xy • 3x2 + 15x • 20abc + 15a2c – 5ac