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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:◦ ax2 + 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◦ 2x2 – 11x = -15
Get everything equal to 0 (add 15 to both sides)◦ 2x2 – 11x + 15 = 0
◦ Last step: Set each parenthesis = 0 and solve(next slide)
-5 -62x2 x x + 15x(2x - 5) -3(2x - 5)
(x - 3)(2x - 5)
+ 2 numbers to:multiply = 30add = -11-5 & -6
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x – 3 = 0 +3 +3x = 3
2x – 5 = 0 +5 +5
2x = 52 2x = 5/2
Optionally: Check your answers2x2 – 11x + 15 = 0
2(3)2 – 11(3) + 15 = 018 – 33 + 15 = 00 = 0
2(5/2)2 – 11(5/2) + 15 = 025/2 – 55/2 + 15 = 00 = 0
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Solve each equation by factoring◦ x2 + 7x = 18
◦ 2x2 + 4x = 6
◦ 16x2 = 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