Factoring Quadratic Trinomials

To Factor Trinomials in the Form x² + bx + c.

OBJECTIVE

C can be positive or negative

Method for Factoring x² + bx + c

The first terms will both be x.Write all the factors of the last termUse addition to find the pair of factors that equal the middle term

Factor completely.x² + 6x + 8(x )(x )

Write all the factors of the last term

1 · 82 · 4

-1 · -8-2 · -4

Since the last term is positive, the signs will be the same

Since the middle term is positive, the signs will be positive.

1 · 82 · 4

1 + 8 = 92 + 4 = 6

+ 2 + 4

Factor Completelyx² - 6x + 8

(x )(x )1 · 82 · 4

-1 · -8-2 · -4

Since the last term is positive the signs will be the same, and the signs will be the same as the middle term

-1 · -8-2 · -4

-1 + (-8) = -9-2 + (-4) = -6

- 2 - 4

Factor Completelyx² + 14x + 40

1 · 40 2 · 204 · 105 · 8

4 + 10 = 14(x + 4)(x + 10)

x² - 10x + 16-1 · -16-2 · -8-4 · -4

-2 + (-8) = -10(x – 2)(x – 8)

Factor Completelyx² + 2x - 8

-1 · 8Since the last term is negative, make sure you list all factors of the last term1 · -8

-2 · 4 2 · -4

-2 + 4 = 2(x – 2)(x + 4)

Factor Completelyx² - x - 20-1 · 20 1 · -20-2 · 10 2 · -10-4 · 5 4 · -5

4 + (-5) = -1( x + 4)(x – 5)

x² + 4x - 21-1 · 21 2 · -21-3 · 7 3 · -7

-3 + 7 = 4

(x – 3)(x + 7)