Factoring Quadratic Expression

Today’s Objective:I can factor a quadratic expression.

First

(𝑥+3)(𝑥+5)

𝑥 (𝑥 )𝑥2+8 𝑥+15

Outer Inner Last

Multiplying Binomial factors:

(2 𝑥−3)(𝑥+7)

2 𝑥2+11𝑥− 21

Factoring when

𝑥2+9𝑥+20Factors of c (20):Add to b (9)

1 ,20 2 ,104 , 521 12 9××

(𝑥+4 )(𝑥+5)+𝑥 (5 )+3 (𝑥)+3 (5) 𝑥2+2𝑥− 15

Factors of c (-15):Add to b (2)

−1 , 15−3 ,514 2×

(𝑥− 3)(𝑥+5)

Tipsc is negative• factors are

oppositeb is positive• larger factor is

positive

𝑥2−11 𝑥+30(𝑥−5)(𝑥−6)

FOIL

Factors: numbers/expressions that have a product equal to the given number/expression

Factoring common factors6 𝑥2+9 𝑥3 𝑥 3 𝑥¿3 𝑥 ()2 𝑥+3

7 𝑥2− 217 7

¿7 ()𝑥2−3

4 𝑥2+20𝑥−564 4¿ 4 ()𝑥2+5 𝑥

4−14

¿ 4 (𝑥+7)(𝑥−2)

−𝑥2+14 𝑥+32¿−1 ()𝑥2−14 𝑥−32¿−1 (𝑥+2)(𝑥− 16)

Factoring when 2 𝑥2+11𝑥+12

Factors of ac (24):Add to b (11)

1 ,24 2 ,123 , 825 1 4 11××

2 𝑥2+3 𝑥+8 𝑥+12𝑥 𝑥 4 4𝑥 ()+4 ()

(2 𝑥+3)(𝑥+4)2 𝑥+3 2 𝑥+3

Factoring when 3 𝑥2−11𝑥− 20

Factors of ac (-60):Add to b (-11)

1 ,− 602 , −303 ,−20−59 −28−17××

3 𝑥2+4 𝑥− 15 𝑥−20𝑥 𝑥−5 −5𝑥 (3 𝑥+4)−5 (3 𝑥+4)

(3 𝑥+4 )(𝑥−5)

4 , −15−11×

4 𝑥2 − 4 𝑥− 3Factors of ac (-12):Add to b (-4)

1 ,− 122 , −6−11 − 4×

4 𝑥2+2𝑥− 6 𝑥−32 𝑥2 𝑥−3−32 𝑥(2𝑥+1)−3 (2 𝑥+1)

(2 𝑥+1)(2 𝑥− 3)Tips for factoring•Factor common factors first• If possible have

p. 221:14-54 evens