2. Chapter 2: Factoring
Chapter 2:
Limits
Chapter 3:
Continuity

3. “Factoring”’ (x – 1)(x + 2) – (x – 1)(2x – 3) 1. Common Factor
ab – ac + ad = a (b – c + d)
*The greatest common factor is the largest number that can divide all the terms of the given expression.
Example:
9x2y2 + 6xy3 + 21x3y3 + 3xy2
(x – 1)(x + 2) – (x – 1)(2x – 3)

4. “Factoring”’ 2(x – 2y)2 – 18z2 2. Difference of Two Squares
a2 – b2 = (a + b)(a – b)
*The factors of a difference of two squares are the sum and difference of the square roots of two perfect squares
Example:
25x2 – 36y2z2
2(x – 2y)2 – 18z2

5. “Factoring”’ 27x3 – 64y3 (2x - y)3 – 8
3. Sum or Difference of Two Cubes
a3 ± b3 = (a ± b)(a2 ab + b2) *
Example:
x9 – 125y3
27x3 – 64y3
(2x - y)3 – 8

6. “Factoring”’ x7 – 128y14 4. Sum or Difference of Odd Powers * Example:

7. “Factoring”’ (2a – 3b)2 – 8(2a – 3b) + 16 5. Perfect Square Trinomial
a2 ± 2ab + b2 = (a ± b)2 *
Example:
4x2 –12xy + 9y2
(2a – 3b)2 – 8(2a – 3b) + 16

8. “Factoring”’ 4m4n2 + 18m2np3 – 10p6 6. Quadratic Trinomial * Example:
acx2 +(ad + bc)x + bd = (ax + b)(cx + d) *
Example:
12x2 + 5x – 3
4m4n2 + 18m2np3 – 10p6

9. “Factoring”’ 7. Factoring by adding and subtracting a perfect square
Example:
4x4 + 8x2y2 + 9y4

10. “Factoring”’ 4c2 – a2 + 2ab – b2 8. Factoring by grouping * Example:
2xy + 8x + 3y + 12
4c2 – a2 + 2ab – b2

11. Example 1:
Factor the following completely:
12xy + 24x2y2 – 15xy2

12. Example 2:
Factor the following completely:
16x4 – 81y4

13. Example 3:
Factor the following completely:
4x2 + 28x + 49

14. Example 4:
Factor the following completely:
x2 – x - 20

15. Example 5:
Factor the following completely:
8x2 – 10x - 7

16. Example 6:
Factor the following completely:
b6 – 64c3

17. Example 7:
Factor the following completely:
x15 – 32

18. Example 8:
Factor the following completely:
x6 + 64

19. Example 9:
Factor the following completely:
4ax – 4ay – 2bx + 2by

20. Example 10:
Factor the following completely:
4a2 – c2 + 12ab + 9b2

21. Example 11:
Factor the following completely:
x3 – 2ax2 - 6a2x + 27a3

22. Example 12:
Factor the following completely:
x4 + 2x2 + 81