= (x + 6) (x + 2)

Factor.

1. x2 +8x + 12

2. x2 +16x + 48

3. x2 - 18x + 32

Multiply

4.(x – 9)(x + 9)

= (x + 12) (x + 4)

= (x - 16) (x - 2)

Factoring Difference of Two Squares

1. Both terms must be Perfect Squares and have a MINUS between them

2. Check the binomial for GCF3. Use two sets of parenthesis (one’s a

plus, one’s a minus)4. Split up what it takes to make the 1st a

perfect square and what it takes the 2nd to be a perfect square

2 2a b a b a b

Difference of Two Squares

Factor21. 25n

5 5n n

22. 4 121x 2 11 2 11x x

Difference of Two Squares

Factor23. 49r 1

7 1 7 1r r

24. 25 36x 5 6 5 6x x

$25,000 Pyramid

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

2 30x x 2 3 40x x 2 15 54x x

2 10 200x x 2 8 48x x

2 9 90x x

(x+1)(x+3) (x+5)(x+3) (x+6)(x+5) (x+4)(x+6)

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

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

(x-15)(x+6)

$25,000 Pyramid

2 6 5x x 2 11 18x x 2 12 32x x 2 16 63x x

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

2 100x 2 5 66x x

2 9 70x x

(x+1)(x+5) (x+9)(x+2) (x+4)(x+8) (x+7)(x+9)

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

(x-10)(x+10) (x-11)(x+6)

(x-14)(x+5)

1. Factor

2x3 + 18x2 + 28x

22 9 14x x x

2 7 2x x x

2. Factor

c4 + 2c3 – 80c2

2 2 2 80c c c

2 10 8c c c

3. Factor

3x2 + 6x – 24

23 2 8x x

3 4 2x x

4. Factor

5x2 + 5x – 10

25 2x x

5 2 1x x

Notes - Solving Quadratic Equations in

Factored Formy = (x + 3)(x + 2)

Ways to solve: y = x2 + 5x + 6

a

acbbx

2

42

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

Solve by FactoringSolve by Factoring

1. Move everything to one side so that the squared term is positive (set equal to zero)

2. Factor (GCF, Trinomial, Grouping, Difference of Two Squares, etc)

3. Solve each factor

4. Check your answer(s)!!!

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 (Find the x-intercepts)

1.) (x+1)(x-3) = 0 2) x(x-2) = 0

3.) (3x-5)(2x+7) = 0

Ex. 2: Solve the equation (x+5)2 = 0

STEP 1: Set the factor equal to zero.

x+5 = 0STEP 2: Solve for x.

x+5 = 0x=-5

STEP 3: Check your answers.(x+5)2= 0

(-5 + 5)2 = 0

(0)2 = 00 = 0

Ex. 3: Solve the equation x2 + 7x + 10 = 0STEP 1: Factor.

(x+5) (x+2) = 0STEP 2, 3: Set each factor to 0, solve for x.

x+5 = 0, x+2 = 0x=-5, -2

STEP 3: Check your answers.

(-5)2 + 7(-5) + 10 = 0

0 = 0

(-2)2 + 7(-2) + 10 = 0

0 = 0

Extension

x feet

(x-4) feet

a) Find an expression for the area.

b) If the area is equal to 5 square feet, find x.

x2 – 4x

x = 5