Special FactoringWe saw previously that (x + 3)(x – 3) = x2 – 9

This helps us to find a special rule for factoring:

a2 – b2 = (a + b)(a – b)

Ex. Factor 25x2 – 16

Ex. Factor x6 – 4y2

Ex. Factor (x + 3)2 – 36

a3 + b3 = (a + b)(a2 – ab + b2)

a3 – b3 = (a – b)(a2 + ab + b2)

Ex. Factor 8p3 – q3

Ex. Factor x3 + 64y3

The sign relationships can help you remember the formulas.

Some trinomials can be made into quadratics using a substitution

Ex. Factor x2y2 – 9xy + 20

Ex. Factor y4 + 8y2 – 48

Solving Equations by FactoringTo solve a quadratic equation, first put everything

on the left to get 0 on the right

Factor the left side

Set each factor equal to 0 and solve for x

IMPORTANT #1: This only works if everything is equal to 0

IMPORTANT #2: Factor means your answer is the parentheses … Solve means you aren’t done until x equals a number

Ex. Solve x2 + x – 12 = 0

Ex. Solve x2 – 3x = 0

Ex. Solve 3x2 + 15x + 12 = 0

Ex. Solve 2x2 – 5x – 12 = 0

Ex. Solve 3x2 + 5x = 2

Ex. Solve (x + 4)(x – 3) = 8

Ex. Solve 3(x2 + 4) + 5 = -6(x2 + 2x) +13

Ex. Solve x3 – x2 – 25x + 25 = 0

Ex. The height of a triangle is 3m less than the base. If the area of the triangle is 20m2, find the height and base of the triangle.

Ex. The altitude of a rocket is modeled by the equation h(t) = -16t2 + 144t. How long does it take for the rocket to return to the ground?