Algebra 1 Common Core Student Edition, Grade 8-9

What information

do you need

before you can

fin d th e o th e r tw o

side lengths?

MATHEMATICAL

PRACTICES

ig R ead y!

A packaging company sells two kinds o f boxes

Box A and Box B. The company is designing

a new box, Box C, that will have the same

volume as Boxes A and B

combined. Suppose one

dimension of Box C is x.

W h at could be th e o th e r

two dimensions? Explain

your reasoning. r 3x + 7

Objective To factor higher-degree polynomials by grouping

MP 1, MP 2, MP 3, MP 4, MP 7

Fact o r i n g b y Gr o u p i n g

@ Common Core State Standards

A-SSE.A.1a Interpret parts o f an expression, such

as terms, factors, and coefficients. Also A-SSE.A.1b,

A-SSE.A.2

Lesson ^
Vocabulary
fa c to rin g by
grouping

Esse n t i a l U n d e r st a n d i n g Some polynomials of a degree greater than 2 can

be factored.

In Lesson 8-6, you factored trinomials of the form ax2 + bx + c by rewriting bx as a

sum of two monomials. You then grouped the terms in pairs, factored the GCF from

each pair, and looked for a common binomial factor. This process is called factoring by^

grouping. You can extend this technique to higher-degree polynomials.

How should you

group the terms of

the polynomial?

First g ro u p th e tw o term s

with the highest degrees.

If that doesn't w ork, try

a n o th e r g ro u p in g. Your

g oal is to fin d a com m on

binomial factor.

Fact o r i n g a Cu b i c Po l y n o m i al

What is the factored form of 3 « 3 — 12n2 + 2n — 8?

3n3 - 12n2 + 2n - 8 = 3 n\n - 4) + 2(n - 4) Factor thaGCF of eachg ro u p o f t w o te rm s.

= (3n2 + 2){n - 4) Factor out the common factor n - 4.

Check (3n2 + 2 ){n - 4) = 3 n3 - 12 n2 + 2n - 8

Go t I t? J. a. What is the factored form of 813 + 14f2 + 201 + 35?

b. Reasoning How is the factoring method used in Problem 1 like

the method used in Lesson 8-6? How is it different?

C

PowerAlgebra.com | Lesson 8-8 Fact oring by Gro up ing 529