# Chapter 2: Factoring Chapter 2: Limits Chapter 3: Chapter 2: Factoring Chapter 2: Limits Chapter 3:

Continuity Factoring 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) Factoring

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 Factoring 3. Sum or Difference of Two Cubes a3 b3 = (a b)(a2 ab + b2)

* Example: x9 125y3 27x3 64y3 (2x - y)3 8

Factoring 4. Sum or Difference of Odd Powers * Example: x5 y5 x7 128y14

Factoring 5. Perfect Square Trinomial a2 2ab + b2 = (a b)2 * Example:

4x2 12xy + 9y2 (2a 3b)2 8(2a 3b) + 16 Factoring 6. Quadratic Trinomial

acx2 +(ad + bc)x + bd = (ax + b)(cx + d) * Example: 12x2 + 5x 3 4m4n2 + 18m2np3 10p6

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

Factoring 8. Factoring by grouping * Example: 2xy + 8x + 3y + 12

4c2 a2 + 2ab b2 Example 1: Factor the following completely: 12xy + 24x2y2 15xy2

Example 2: Factor the following completely: 16x4 81y4 Example 3: Factor the following completely:

4x2 + 28x + 49 Example 4: Factor the following completely: x2 x - 20

Example 5: Factor the following completely: 8x2 10x - 7 Example 6: Factor the following completely:

b6 64c3 Example 7: Factor the following completely: x15 32

Example 8: Factor the following completely: x6 + 64 Example 9:

Factor the following completely: 4ax 4ay 2bx + 2by Example 10: Factor the following completely:

4a2 c2 + 12ab + 9b2 Example 11: Factor the following completely: x3 2ax2 - 6a2x + 27a3

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