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

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Factoring Difference of Two Squares 1.Both terms must be Perfect Squares and have a MINUS between them 2.Check the binomial for GCF 3.Use two sets of parenthesis (ones a plus, ones a minus) 4.Split up what it takes to make the 1 st a perfect square and what it takes the 2 nd to be a perfect square

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Difference of Two Squares Factor

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Difference of Two Squares Factor

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$25,000 Pyramid (x+1)(x+3)(x+5)(x+3)(x+6)(x+5)(x+4)(x+6) (x-6)(x+5) (x-8)(x+5) (x-18)(x+3) (x-20)(x+10) (x-12)(x+4) (x-15)(x+6)

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$25,000 Pyramid (x+1)(x+5)(x+9)(x+2)(x+4)(x+8)(x+7)(x+9) (x-5)(x+4) (x-6)(x+3) (x-13)(x+3) (x-10)(x+10) (x-11)(x+6) (x-14)(x+5)

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1. Factor 2x x x

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2. Factor c 4 + 2c 3 – 80c 2

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3. Factor 3x 2 + 6x – 24

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4. Factor 5x 2 + 5x – 10

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

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Notes - Solving Quadratic Equations in Factored Form 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 = 00 * 3 = 00 * 0 = 0

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Solve by Factoring 1.Move everything to one side so that the squared term is positive (set equal to zero) 2.Factor (GCF, Trinomial, Grouping, Difference of Two Squares, etc) 3.Solve each factor 4.Check your answer(s)!!!

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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 = 2 x+3 = 0 x=-3 STEP 3: Check your answers. (x-2)(x+3) = 0 (2-2)(2+3) = 0 (0)(5) = 0 0 = 0 (x-2)(x+3) = 0 (-3-2)(-3+3) = 0 (-5)(0) = 0 0 = 0

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Solve (Find the x-intercepts) 1.) (x+1)(x-3) = 02) x(x-2) = 0 3.) (3x-5)(2x+7) = 0

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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

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Ex. 3: Solve the equation x 2 + 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 0 = 0 (-2) 2 + 7(-2) + 10 = 0 0 = 0

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Extension x feet (x-4) feet a)Find an expression for the area. b)If the area is equal to 5 square feet, find x. x 2 – 4x x = 5

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