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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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2.4 Equations with Variables on Both Sides To solve an equation with variables on both sides, you must use the Addition or Subtraction Properties of Equality.

2.4 Equations with Variables on Both Sides To solve an equation with variables on both sides, you must use the Addition or Subtraction Properties of Equality.

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