Notes - Solving Quadratic Equations in Factored Form

If ab = 0, then a = 0 or b = 0

If the product of two factors is zero, then at least one of the factors must be zero.

3 * 0 = 0 0 * 3 = 0 0 * 0 = 0

Notes - Solving Quadratic Equations in

Factored Form(x + 3)(x + 2) = 0

Ex. 1: Solve the equation (x-2)(x+3) = 0STEP 1: Set each factor equal to zero.

x-2= 0 and x+3 = 0STEP 2: Solve for x.

x-2= 0

x = 2

x+3 = 0

x=-3

STEP 3: Check your answers.(x-2)(x+3) = 0(2-2)(2+3) = 0

(0)(5) = 00 = 0

(x-2)(x+3) = 0(-3-2)(-3+3) = 0

(-5)(0) = 0

0 = 0

Solve

1) x2 + 5x + 6 = 0

2) x2 – 2x – 8 = 0

3) x2 + 7x + 6 = 0

4) 3x(2x + 5) = 0

Answers

1) x = -3, -2

2) x = -2, 4

3) x = -1, -6

4) x = 0, -5/2

$25,000 Pyramid

$25,000 Pyramid

2 4 3x x 2 8 15 0x x 2 11 30 0x x 2 10 24x x

2 30 0x x 2 3 40x x

2 15 54 0x x

2 10 200 0x x 2 8 48x x

2 9 90 0x x

(x+1)(x+3) x = -5, -3 x = -6, -5 (x+4)(x+6)

x = 6, x-5 (x-8)(x+5) x = 18, -3

x =20, -10 (x-12)(x+4)

x=15, -6

$25,000 Pyramid

2 6 5x x 2 11 18 0x x 2 12 32x x

2 16 63 0x x

2 20x x 2 3 18x x 2 10 39x x

2 100x 2 5 66 0x x

2 29 70x xy y

(x+1)(x+5) X=-9, -2 (x+4)(x+8) x= -7, -9

(x-5)(x+4) (x-6)(x+3) (x-13)(x+3)

(x-10)(x+10) X=11, x=-6

(x-14y)(x+5y)