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**6.8 Solving Equations by Factoring**

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**Zero Product Property Rule if (a)(b) = 0, then a = 0 or b = 0**

Zero Product Property Rule if (a)(b) = 0, then a = 0 or b = 0. if a = 0 or b = 0, then (a)(b) = 0.

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the quest for “X” X

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Solving for X If the equation is already factored and set equal to 0 then: set each factor equal to 0 solve

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**What values of “x” make this equation true? (x + 1)(x – 7) = 0**

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**What values of “x” make this equation true? x(2x – 9) = 0**

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**What values of “x” make this equation true? (x + 3)(x – 4) = 0**

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**What values of “x” make this equation true? (x - 7)(x – 3) = 0**

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**What values of “y” make this equation true? y(3y – 17) = 0**

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**If the equation is not already factored then you need to:**

Solving for X If the equation is not already factored then you need to: set it =0 factor it set each of its factors =0, solve for x

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**Solve for “y”: y2 + 5y = -6 Add 6 to get “0” on one side Factor**

Let each factor = zero

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Solve for “y”: y2 – 8y = -16 Add 16 to get “0” on one side Factor

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x2 – x – 6 = 0 x = 3 or (-2)

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m2 – m = 56 m = 8 or (-7)

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k2 – 3k = 28 m = 7 or (-4)

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“root” For a polynomial containing a variable, any value of the variable that makes the value of the polynomial = zero is called a “root” of the polynomial. Find the roots of x2 – 5x = 0

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Find the roots of 25x2 – 16

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**Assignment Page 289 (2-68) even**

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