= (x + 6) (x + 2) 1. x2 +8x x2 +16x + 48 = (x + 12) (x + 4)

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= (x + 6) (x + 2) 1. x2 +8x + 12 2. x2 +16x + 48 = (x + 12) (x + 4) Factor. = (x + 6) (x + 2) 1. x2 +8x + 12 2. x2 +16x + 48 3. x2 - 18x + 32 Multiply 4.(x – 9)(x + 9) = (x + 12) (x + 4) = (x - 16) (x - 2)

Factoring Difference of Two Squares Both terms must be Perfect Squares and have a MINUS between them Check the binomial for GCF Use two sets of parenthesis (one’s a plus, one’s a minus) Split up what it takes to make the 1st a perfect square and what it takes the 2nd to be a perfect square

Difference of Two Squares Factor

Difference of Two Squares Factor

$25,000 Pyramid (x-15)(x+6) (x-20)(x+10) (x-12)(x+4) (x-6)(x+5)

$25,000 Pyramid (x-14)(x+5) (x-10)(x+10) (x-11)(x+6) (x-5)(x+4)

1. Factor 2x3 + 18x2 + 28x

2. Factor c4 + 2c3 – 80c2

3. Factor 3x2 + 6x – 24

4. Factor 5x2 + 5x – 10

Notes - Solving Quadratic Equations in Factored Form y = (x + 3)(x + 2) Ways to solve: y = x2 + 5x + 6

Notes - Solving Quadratic Equations in Factored Form Zero Product Property If ab = 0, then a = 0 or b = 0 If the product of two factors is zero, then at least one of the factors must be zero. 3 * 0 = 0 0 * 3 = 0 0 * 0 = 0

Solve by Factoring Move everything to one side so that the squared term is positive (set equal to zero) Factor (GCF, Trinomial, Grouping, Difference of Two Squares, etc) Solve each factor Check your answer(s)!!!

Ex. 1: Solve the equation (x-2)(x+3) = 0 STEP 1: Set each factor equal to zero. x-2= 0 and x+3 = 0 STEP 2: Solve for x. x-2= 0 x+3 = 0 x=-3 x = 2 STEP 3: Check your answers. (x-2)(x+3) = 0 (x-2)(x+3) = 0 (2-2)(2+3) = 0 (-3-2)(-3+3) = 0 (-5)(0) = 0 (0)(5) = 0 0 = 0 0 = 0

Solve (Find the x-intercepts) 1.) (x+1)(x-3) = 0 2) x(x-2) = 0 3.) (3x-5)(2x+7) = 0

Ex. 2: Solve the equation (x+5)2 = 0 STEP 1: Set the factor equal to zero. x+5 = 0 STEP 2: Solve for x. x+5 = 0 x=-5 STEP 3: Check your answers. (x+5)2= 0 (-5 + 5)2 = 0 (0)2 = 0 0 = 0

Ex. 3: Solve the equation x2 + 7x + 10 = 0 STEP 1: Factor. (x+5) (x+2) = 0 STEP 2, 3: Set each factor to 0, solve for x. x+5 = 0, x+2 = 0 x=-5, -2 STEP 3: Check your answers. (-5)2 + 7(-5) + 10 = 0 (-2)2 + 7(-2) + 10 = 0 0 = 0 0 = 0

Extension (x-4) feet x feet x2 – 4x Find an expression for the area. If the area is equal to 5 square feet, find x. x = 5