1. Factoring Completely

2. Your factoring tools Factoring a GCF
Factoring the difference of two perfect squares
Factoring quadratic trinomials (A=1)
Factoring quadratic trinomials (A>1)

3. Factoring a GCF
Find the greatest common factor and factor it out of the polynomial
Make sure to divide everything by the GCF
Examples:
1) 3x + 6
3(x + 2)
2) x3 - 5x2 + 7x
x(x2 - 5x + 7)
3) 15x5 + 25x3
5x3(3x2 + 5)

4. Factoring the difference of two perfect squares
Is the first term a perfect square?
Is the last term a perfect square?
Is the sign between them a minus sign?
Examples:
1) x2 - 49
(x + 7)(x - 7)
2) 25x2 - 81
(5x + 9)(5x - 9)
3) x
(x2 + 11)(x2 - 11)
4) 16x y2
(4x3 + 15y)(4x3 - 15y)

5. Factoring quadratic trinomials (A=1)
X Method (or Guess and Check or Box Method)
Examples:
1) x2 + 10x + 9
(x + 1)(x + 9)
2) x2 - 11x + 30
(x - 5)(x - 6)
3) x2 - 16x - 36
(x - 18)(x + 2)

6. Factoring quadratic trinomials (A>1)
Umbrella-Method
3) 3x2 + 8x + 5
4) 6x2 + 5x - 4

7. Factoring completely (using more than one tool)
1) 7x2 - 28
7(x2 - 4)
7(x + 2)(x - 2)

8. Factoring completely (using more than one tool)
2) 20x3 - 5x
5x(4x2 - 1)
5x(2x + 1)(2x - 1)

9. Factoring completely (using more than one tool)
3) x4 - 81
(x2 + 9)(x2 - 9)
(x2 + 9)(x + 3)(x - 3)

10. Factoring completely (using more than one tool)
4) 4x2 - 16x + 16
4(x2 - 4x + 4)
4(x - 2)(x - 2)

11. Factoring completely (using more than one tool)
5) 6x3 + 18x2 - 24x
6x(x2 + 3x - 4)
6x(x + 4)(x - 1)

12. Factoring completely (using more than one tool)
6) 15x2 - 2x - 8
(3x + 2)(5x - 4)

13. Factoring completely *7) 12x2 + 3x - 9 Factor the GCF first !!!