Essential Question:How is factoring used to solve quadratic

equations?

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

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

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

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

Assignment◦ Page 270◦ 1 – 10 (all problems)

Solve all problems by factoring (not square roots)◦ No work = no credit