Algebra 1 Common Core Student Edition, Grade 8-9

Getting Ready!

4 MUSEUM

ADM ISSIO N: $ 1 5 PER PERSON

PARKING: $5 PER CAR

AQUARIUM t

ADMISSION: $20 PER PERSON

PARKING: $ 6 PER CAR

Try breaking

th is problem into

simpler parts.

How much do

th e y spend on

admission? On

parking?

MATHEMATICAL

PRACTICES

Adding and Subtracting

Po l y n o m i al s

Objective To classify, add, an d subtract polynom ials

Co m m o n Co r e St at e St a n d a r d s

A -AP R.A .1 Understand that polynomials form a

system analogous to the integers, namely, they are

closed under the operations of addition, subtraction, and

multiplication: add, subtract, and multiply polynomials.

M P 1, M P 2, M P 3, M P 4, M P 6

Lesson

Vocabulary

• monomial


• degree o f a
  monomial


• polynomial


• standard form of
  a p o ly n o m ia l


• degree of a
  polynomial


• binomial


• trinom ial

W h y is th e d e g re e o f

a nonzero constant 0?

You can w rite a nonzero

co n sta n t c as cx°. The

e x p o n e n t is 0 , so t h e

degree is 0 also.

In som e cases, you can m odel a situation w ith an expression com posed of monomials.

A monomial is a real num ber, a variable, or a p ro d u c t of a real n u m b e r a n d one or m ore

variables w ith w h o le-n u m b er exponents. Here are som e exam ples of m onom ials.

18 z -4x2 2.5xy

Esse n t i a l U n d e r s t a n d i n g You can use m onom ials to form larger expressions

called polynomials. Polynom ials can be ad d e d a n d subtracted.

The degree of a monomial is th e sum of th e exponents of its variables. The degree of a

nonzero constant is 0. Zero has no degree.

Fi n d i n g t h e D e g r ee o f a M o n o m i al

W hat is th e d eg ree o f e a ch m o n o m ia l?

Q 5 x D e g re e : 1 5x = 5x1. The exponent is 1.

06x3y2 D e g re e : 5 The exponents are 3 and 2. Their sum is 5.

0 4 Degree: 0 4 = 4x°. The degree o f a nonzero constant is 0.

Go t It? 1. W hat is th e degree of each m onom ial?

a. 8 xy b. — 7y4z c. 11

486 Chapter 8 Polynomials and Factoring