Algebra 1 Common Core Student Edition, Grade 8-9

@ Common Core State Standards

vr2 _L ( w J - S' A-SSE.A.1 a Interpret parts of an expression, such as

r U C l O i 11 I U A I U A I L terms, factors, and coefficients.

MP 1, MP 3, MP 4, MP 7, MP 8

Objective To factor trinom ials of th e form x 2 + bx + c

Get t i n g Read y!

H e re 's a h in t.

What two numbers

have a sum o f 7 and

a p ro d u c t o f 12?

The area of t he rect angular solar panel is given

by the trinomial x 2 + 7x + 12. The height of the

so l ar panel is x + 3. W h at is an ex p r essio n f o r

the length of the panel? Explain your reasoning.

MATHEMAIICAL

PRACTICES Esse n t i a l U n d e r st a n d i n g You can w rite som e trinom ials of th e form x + bx + c

as th e p ro d u ct of two binom ials.

To u n d e rsta n d how, consider th e p ro d u c t of binom ials below.

(x + 3)(x + 7) = x 2 + (7 + 3)x + 3 • 7 = x2 + lOx + 21

The coefficient of the trinom ial's x2-te rm is 1. The coefficient of the trinom ial’s x-term,

10, is th e sum of th e n u m b ers 3 a n d 7 in th e binom ials. The trinom ial’s co n stan t term ,

21, is the product of th e sam e num bers, 3 an d 7. To factor a trinom ial of the form

x2 + bx+ c as the p ro d u c t of binom ials, you m u st find two n u m b ers th at have a sum of

b an d a p ro d u ct of c.

W h a t is an easy w a y

to organize your

factoring?

Use a ta b le to lis t th e

pairs o f fa cto rs o f th e

co n sta n t te rm c and th e

sums o f those pairs of

factors.

1 jl Got It? 1. W hat is the factored form of r 2 + l l r + 2 4?

Fact o r i n g x 2 + b x + c W h e r e b > 0 , c > 0

W hat is th e fa c to re d fo rm of x 2 + 8x + 15?

List the pairs of factors of 15. Identify the

p air th at has a sum of 8.

x 2 + 8x + 15 = (x + 3)(x + 5)

Check (x + 3)(x + 5) = x 2 + 5x + 3x + 15

= x 2 + 8x + 15

■ 2:1* 01 i l. 1

1 a n d 1 5 16

3 and 5 8

Pr o b l em 1

5 1 2 Chapter8 Polynomials and Factoring