DO NOW: FACTOR

1) x2 – 196

2) 4x2 + 38x + 34

3) 16x2 – 36

1) (x + 14)(x – 14)

2)2(2x+17)(x+1)

3)4(2x+3)(2x-3)

SOLVE QUADRATIC EQUATIONS

BY FACTORING

THINK, PAIR, SHARE

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

ZERO PRODUCT PROPERTY

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

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.

YOU TRY IT …

1) (x – 2)(x + 3) = 0

2) (x + 5)2 = 0

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

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

PRACTICE

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

SUM IT UP ….

How do you solve a quadratic equation by factoring?