1. Factoring by GCF
CA 11.0

2. Objective - To factor a polynomial by finding the GCF

3. Factoring Polynomials
Four Types of Factoring:
Greatest Common Factor
Difference of Two Squares
Perfect Square Trinomial
Trinomial Factoring: ax2 +bx + c

4. FACTORING
The FIRST step to factoring ANY polynomial is to find the GCF and the LEFTOVERS.
If you make a factor tree, finding the leftovers is easy.
Otherwise, you can divide to find the leftovers.
If nothing is leftover, you MUST write down the invisible factor of 1!

5. FACTORING Factor the polynomial: 4x2 - 3x
Write each term out the long way (prime factorization)
4x2 = · 2 · x · x
-3x = (-1) · · x
The GCF is x
x( )
The leftovers for 4x2 are 2 · 2 · x = 4x
The leftovers for -3x are (-1) · 3 = –3 4x
- 3

6. FACTORING Factor the polynomial: 10y3 + 20y2 - 5y
Write each term out the long way (prime factorization)
10y3 = · 5 · y · y · y
+ 20y2 = +2 · 2 · 5 · y · y
- 5y = (-1) · 5 · y
The GCF is 5y
5y( )
The leftovers for 10y3 are 2 · y · y = 2y2
The leftovers for + 20y2 are +2 · 2 · y = +4y
The leftovers for - 5y are -1
2y2
+4y
- 1

7. Try these!
-12x - 8x2 5x2 + 7

8. Common Binomial Factors
7(x - 3) - 2x(x - 3)
What is common to both terms?
(x - 3)
(x - 3) ( )
What is leftover? 7
- 2x

9. Common Binomial Factors
- t(t2 + 4) + (t2 + 4)
What is common to both terms?
(t2 + 4)
(t2 + 4)( )
What is leftover?
- t
+ 1

10. Try these!
9x(x + 3) - 5(3 + x) -3x2(x + 7) + 4(x - 7)