VocabularyMonomial – Polynomial with 1 term.Binomial – Polynomial with 2 terms.Trinomial – Polynomial with 3 terms.

VocabularyMonomial – a number, a variable with a

positive integer exponent, or the product of a number and one or more variables with positive integer exponents.

Degree of a monomial – sum of the exponents of the variables in the monomial

VocabularyPolynomial – a monomial or a sum of

monomials, each called a term of the polynomial.

Degree of a polynomial – the greatest degree of its terms.

Leading coefficient – the coefficient of the highest degree term.

Rewrite a polynomial

Write so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial.

Example 1

315x +x3–

SOLUTION

The polynomial can be written as . The table shows the degree of each term. The greatest degree is 3, so the degree of the polynomial is 3, and the leading coefficient is .

15x+x3– 3+

1–

Term

Degree

15x 3

3 1 0

x3–

Identify and classify polynomials

Tell whether the expression is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial.

Example 2

Expression Is it a polynomial? Classify by degree and number of terms

9 Yes 0 degree monomiala.

Yes 2nd degree trinomialb. x2x2 + 5–

No; variable exponentc.

No; negative exponentd.

6n4 8n–

Yes 5th degree binomiale. 4b4c7bc3 +

n–2 3–

Adding & Subtracting PolynomialsTo add polynomials, combine like terms.

To subtract a polynomial, add its opposite

To find the opposite of a polynomial, multiply

each of its terms by -1

Add and subtract monomials

Find the sum or difference.

Example 3

a. 7b2+3b2–

5xy2xy –b.

4b2= Combine like terms.

+= 2xy 5xy–( ) Rewrite as a sum.

= 3xy– Combine like terms.

Add polynomials

Find the sum

Example 4

x3x2 + 6–( ) 4x+x2 10+( ).+

= x23x2 +( ) + 4x+x( ) 10+ )+ ( 6–

= 5x+4x2 4+

x3x2 + 6–( ) 4x+x2 10+( )+

SOLUTION

Group like terms and simplify.

Multiple Choice PracticeExample 5

3x4x2 5+( )– – x3x2 8( )– =

4xx2 3– – 2xx2 3– –

4xx2 13– +2xx2 13– +

= 3x4x2 5+– – x3x2 8++

= 3x24x2( – ) 3x x+ )(+ – ( )8+5+

= 2xx2 13– +

–

SOLUTION

3x4x2 5+( )– – x3x2 8( )– –

Multiple Choice PracticeExample 5

ANSWER The correct answer is C.