Quadratics:Factoring

Polynomials

Name:________________________

Steps:

1. GCF – Any number of terms

2. Four Terms – Grouping

3. Three Terms – Trinomial Rules

4. Two Terms – Difference of 2 Squares

Greatest Common Factora. 3x2 + 15x

b. 10a2 + 4a

c. 14m2n – 2mn

Four Terms – Grouping

a. y3 + 7y2 + 2y + 14

b. x3 – 4x2 – 6x + 24

c. x(x + 2) – 12(x + 2)

Sign Rules

Factoring Trinomials Sign Rules

If the last term is POSITIVE:

If the last term is NEGATIVE:

Both signs will be the SAME as the middle

term.

Signs will be DIFFERENT in the

parentheses.

( + )( + )or

( −¿ )( −¿ )( + )( −¿ )

If b is POSITIVE, then the larger factor needs to be positive

If b is NEGATIVE, then the larger factor will need to be

Three Terms – Trinomials when a = 1a. x2 + 10x + 16

b. x2 – 12x + 27

c. 2m2 + 4m – 48

d. –n2 + 12n - 36

Three Terms – Trinomials when a > 1a. 3y2 + 5y + 2

b. 2m2 + m – 21

c. 6x2 – 13x + 2

Perfect Trinomialsa. n2 – 12n + 36

b. x2 + 10x + 25

c. a2 – 2a + 1

Two Terms – Difference of Squares

a. x2 – 25

b. 2t2 – 8

c. x2 + 36

d. 4x2 – 25

e. 49 – 9m2

ALWAYS in the form: (x + y)(x – y)Think conjugates to cancel the middle terms!

Solve by Square Rootsa. x2 – 7 = 9 b. 4r2 – 7 = 9

c. 36x2 = 121 d. 7x2 – 8 = 13

e. 4z2 + 7 = 12 f. (x + 2)2 = 10

g. 2(x – 3)2 = 18

Solve by Quadratic Formulax=−b±√b2−4ac

2a

a. x2 + 7x + 12 = 0 b. 4x2 – 4x + 1 = 0

c. 4x2 + 8x – 1 d. -2x2 – 2x = 1

Completing the Squarea. x2 – 10x + 13 = 0

b. x2 – 8x + 7 = 0

c. 3x2 – 12x + 27 = 0

d. 2x2 – 20x + 24 = 0