Basic Mathematics for College Students

A-5

Polynomials

APPENDIX

II

SECTION II.1

Introduction to Polynomials

Objectives

1 Know the vocabulary for

polynomials.

2 Evaluate polynomials. Know the vocabulary for polynomials.

Recall that analgebraic term,or simply aterm,is a number or a product of a number

and one or more variables, which may be raised to powers. Some examples of terms are

17, 5 x,6t^2 , and  8 z^3

The coefficientsof these terms are 17, 5, 6, and 8, in that order.

Polynomials

A polynomialis a single term or a sum of terms in which all variables have

whole-number exponents and no variable appears in the denominator.

Some examples of polynomials are

141, 8 y^2 ,2x1, 4 y^2  2 y3, and 7 a^3  2 a^2 a 1

The polynomial 8y^2 has one term. The polynomial 2x1 has two terms, 2xand 1. Since

4 y^2  2 y3 can be written as 4y^2 ( 2 y) 3, it is the sum of three terms, 4y^2 , 2 y,

and 3.

We classify some polynomials by the number of terms they contain. A polynomial

with one term is called a monomial.A polynomial with two terms is called a binomial.

A polynomial with three terms is called a trinomial.Some examples of these

polynomials are shown in the table below.

1

Monomials Binomials Trinomials

5 x^22 x 15 t^2  4 t 3

 6 x 18 a^2  4 a 27 x^3  6 x 2

29  27 z^4  7 z^232 r^2  7 r 12

EXAMPLE (^1) Classify each polynomial as a monomial, a binomial, or a
trinomial: a. 3 x 4 b. 3 x^2  4 x 12 c. 25 x^3
StrategyWe will count the number of terms in the polynomial.
WHYThe number of terms determines the type of polynomial.
Solution
a.Since 3x4 has two terms, it is a binomial.
b.Since 3x^2  4 x12 has three terms, it is a trinomial.
c. Since 25x^3 has one term, it is a monomial.
Self Check 1
Classify each polynomial as
a monomial, a binomial, or
a trinomial:
a. 8 x^2  7
b. 5 x
c. x^2  2 x 1
Now TryProblems 5, 7, and 11