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Special Factoring We saw previously that (x + 3)(x – 3) = x 2 – 9 This helps us to find a special rule for factoring: a 2 – b 2 = (a + b)(a – b) Ex. Factor.

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Presentation on theme: "Special Factoring We saw previously that (x + 3)(x – 3) = x 2 – 9 This helps us to find a special rule for factoring: a 2 – b 2 = (a + b)(a – b) Ex. Factor."— Presentation transcript:

1 Special Factoring We saw previously that (x + 3)(x – 3) = x 2 – 9 This helps us to find a special rule for factoring: a 2 – b 2 = (a + b)(a – b) Ex. Factor 25x 2 – 16

2 Ex. Factor x 6 – 4y 2 Ex. Factor (x + 3) 2 – 36

3 a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) Ex. Factor 8p 3 – q 3 Ex. Factor x y 3 The sign relationships can help you remember the formulas.

4 Some trinomials can be made into quadratics using a substitution Ex. Factor x 2 y 2 – 9xy + 20

5 Ex. Factor y 4 + 8y 2 – 48

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7 Solving Equations by Factoring To 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 arent done until x equals a number

8 Ex. Solve x 2 + x – 12 = 0 Ex. Solve x 2 – 3x = 0 Ex. Solve 3x x + 12 = 0

9 Ex. Solve 2x 2 – 5x – 12 = 0

10 Ex. Solve 3x 2 + 5x = 2

11 Ex. Solve (x + 4)(x – 3) = 8

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

13 Ex. Solve x 3 – x 2 – 25x + 25 = 0

14 Ex. The height of a triangle is 3m less than the base. If the area of the triangle is 20m 2, find the height and base of the triangle.

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


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