Algebra 1 Common Core Student Edition, Grade 8-9

Some factorable trinom ials have a negative coefficient of x an d a positive constant

term. In this case, you n e e d to inspect the negative factors of c to find the factors of

the trinomial.

Why look at pairs
of negative factors
of 24?
You w a n t th e fa ctors o f
2 4 w ith a sum o f —11.
Only tw o negative
num bers have a p o sitive
product and a n e g ative
sum.

Pr o b l em 2 Fa ct o r i n g x 2 + bx + c W h e r e b < 0, c > 0

What is the factored form of x2 - 1 l x + 2 4?

List th e pairs of negative factors of 24. Identify th e p a ir th a t has a sum of - 1 1.

-1 and - 2 4

-2 and -12

-3 and - f

-4 and - 6

-25

-14

-11 ✓

-10

x 2 - l l x 4- 24 = (x - 3)(x - 8)

Check (x - 3)(x - 8) = x 2 - 8x - 3x + 24

= x 2 - l l x + 24

fcjfr G o t It? 2. a. W hat is th e factored form of j/2 - 6y 4- 8?

b. Reasoning Can you factor x 2 — x 4- 2? Explain.

Think
What's another way
to do this problem?
Find tw o positive factors
o f 15 th a t differ by 2. The
factors are 3 and 5. Then
attach a negative sign to
one o f the factors so th a t
th e ir sum is positive. You
get - 3 and 5.

W hen you factor trinom ials w ith a negative co n stan t term , you n e e d to inspect pairs of

positive an d negative factors of c.

Pr o b l em 3 Fact o r i n g x 2 4- bx 4- c W h er e c < 0

What is the factored form of x 2 4- 2x — 15?

Identify th e p air of factors of - 1 5 th a t has a sum of 2.

r.. 4

1 a n d - 1 5 -1 4

-1 and 15 14

3 and - 5 -2

-3 and 5 2

x2 + 2x - 15 = (x - 3)(x 4- 5)

* G ot It? 3. W hat is th e factored form of each polynom ial?

a. n2 4- 9n — 36 b. c2 — 4c — 21

PowerAlgebra.com 1 L e s s o n 8 - 5 Fac t o r i n g x? + bx + c 513