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Essential Question: How is factoring used to solve quadratic equations?

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The standard form of a quadratic equation is: ◦ ax 2 + bx + c = 0 We can solve some quadratic equations by factoring ◦ We’ll solve non-factorable equations after we come back from break We solve a factored quadratic equation because of the Zero-Product Property ◦ If ab = 0, then a = 0 or b = 0 Example: If (x + 3)(x – 7) = 0, then x = -3 or x = 7 Take each parenthesis, set it equal to 0 and solve for x

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Solve by factoring ◦ 2x 2 – 11x = -15 Get everything equal to 0 (add 15 to both sides) ◦ 2x 2 – 11x + 15 = 0 ◦ Last step: Set each parenthesis = 0 and solve (next slide) -5-62x 2 x x + 15 x(2x - 5) -3(2x - 5) (x - 3)(2x - 5) + 2 numbers to: multiply = 30 add = -11 -5 & -6

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x – 3 = 0 +3 +3 x = 3 2x – 5 = 0 +5 +5 2x = 5 2 2 x = 5 / 2 Optionally: Check your answers 2x 2 – 11x + 15 = 0 2(3) 2 – 11(3) + 15 = 0 18 – 33 + 15 = 0 0 = 0 2( 5 / 2 ) 2 – 11( 5 / 2 ) + 15 = 0 25 / 2 – 55 / 2 + 15 = 0 0 = 0

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Solve each equation by factoring ◦ x 2 + 7x = 18 ◦ 2x 2 + 4x = 6 ◦ 16x 2 = 8x x = 2 or x = -9 x = 1 or x = -3 x = 0 or x = ½

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Assignment ◦ Page 270 ◦ 1 – 10 (all problems) Solve all problems by factoring (not square roots) ◦ No work = no credit

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