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

“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)

“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

“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

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

“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

“Factoring”’ 4m4n2 + 18m2np3 – 10p6 6. Quadratic Trinomial * Example: 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”’ 4c2 – a2 + 2ab – b2 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