1. Try to find the middle through trial and error
Factoring
Greatest Common Factor 2
5x- 15x = 5x(1-3x) 2 4 3
Grouping
5x – 10x – 2x + 4
5x (x – 2) – 2(x - 2)
(5x – 2) (x – 2)
Difference of Squares
a b = (a – b) (a+b)
4x – 49 = (2x – 7)(2x + 7)
Difference of Cubes
a + b = (a + b) (a + ab + b )
8x – 1 = (2x – 1)(4x + 2x + 1)
Reverse Foil
Try to find the middle through trial and error
Ax + Bx + c or Ax + Bx + c
( ) = ( + ) ( + )
( ) = ( - ) ( - )
( ) = ( - )( + ) or (+)(-)
( ) = ( - )( + ) or (+)(-) 3 2 2 2 2 2 2 4 2 2 2 - 2 3 3 3 2

2. Factoring Polynomials
Different Ways to Factor
GCF (Greatest Common Factor)
Grouping
Reverse Foil
Calculator with Grouping
Cube Pattern

3. GCF
Factor 4x²y + 8x³y.
What is the largest thing that both terms have in common?
What should we do when we find the GCF?
Write it in its factored form.

4. Factor the following 20a²b³ + 30a5b² 33p4r³ - 9pr³
45xyz³ - 36x³yz + 18xy³z

5. Grouping A lot like GCF, just group terms first. 4xy + 2x + 6y + 3
21 – 7t + 3r – rt
4x² - 4xy + 8x – 8y

6. Reverse Foil Works with TRInomials Always look for a GCF first!!!
x² + 5x + 6
Using what you already know about FOIL, try to come up with a basic idea of what the factored form would look like.

7. Factor Each Expression
x² + 7x + 6
x² - 6x + 8
x² + 11x + 24
x² - 7x – 18
x² + 3x – 10
x² - 4x – 12
2x² + 3x + 1

8. Special case in factoring…
Factor x² - 9
How could we re-write x² - 9?
Now factor.
x² - 100
4x² - 49

9. Now for some fun ones…
3x² - 27y²
p4 – 1
y4 – 81
3x² - 3y²

10. What about polynomials with leading coefficients?
Factor 2x² + 5x + 3.
Here’s a shortcut…
a●c (2 ●3=6)
Rewrite as x² + 5x + 6, then factor.
(x + )(x + )

11. Then divide out the 2 we originally multiplied (it was the coefficient of the x²).
(x + 3/2)(x + 2/2)
“Reduce” the fractions and if there is still a denominator, put it in the front.

12. Factor the following polynomials.
5x² + 34x + 24
6x² + x – 15
15x² + 26x + 8
4x² - 22x + 30 (hint: find a GCF first)

13. Factor 8x³ - 1
Take the cube root of each term
Cube root of 8x³ = 2x
Cube root of -1 = -1
(2x – 1)
Square each of those and put them in a trinomial at the beginning and end
(4x )

14. (2x – 1)(4x )
Multiply the terms from the binomial and change the sign
2x●-1 = -2x 2x
Put that in the middle of the trinomial
(2x – 1)(4x + 2x + 1)

15. Factor the following
8x³ + 27
x³ - 64
x³ + 8y³
-27x³ + 8