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Published byBlake Nicholson Modified over 4 years ago

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**Do Now: Factor x2 – 196 4x2 + 38x + 34 16x2 – 36 (x + 14)(x – 14)**

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**Solve Quadratic Equations by Factoring**

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**If ab = 0, what must be true about the values of a and/or b?**

Think, pair, share If ab = 0, what must be true about the values of a and/or b?

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**For any real numbers a and b, if ab=0, then either a=0, b=0, or both.**

Zero Product Property For any real numbers a and b, if ab=0, then either a=0, b=0, or both.

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**Example 1 (x+3)(2x-1) = 0 x + 3 = 0 OR 2x – 1 = 0 x = -3 OR x = ½**

Equation in factored form and equals zero Use Zero Product Property to solve, simply set the individual factors equal to zero.

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You try it … 1) (x – 2)(x + 3) = 0 2) (x + 5)2 = 0

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**What if you have a standard form equation?**

18x2 – 3x – 1 = 0 (6x + 1)(3x – 1) = 0 6x+1=0 OR 3x-1=0 x= -1/6 or x = 1/3 Check that equation equals zero, if not rewrite Factor Solve using Zero Product Property Check your work

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**What if the equation does not equal zero?**

x2 – 27 = 6x x2 – 6x – 27 = 0 (x-9)(x+3) = 0 x – 9 = 0 OR x + 3 = 0 x = 9 OR x = -3 Check that equation equals zero, if not rewrite Factor Solve using Zero Product Property Check your work

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practice x2 – 4x = 5 3x2 + 7x – 6 = 0 9x2 – 24x + 16 = 0 x2 – 63 = 2x

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**How do you solve a quadratic equation by factoring?**

Sum it up …. How do you solve a quadratic equation by factoring?

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