13.01

Polynomials and Their Degree

A polynomial is the sum or difference of monomials.

x + 3

Examples:

Remember, a monomial is a number, a variable, or a product of both.

x2 – 6x 3x2 – x + 2

An expression is not a polynomial when any of its terms are divided by a variable.

Each monomial is a term of the polynomial.

Examples:

x

1

1

3

x y

26

A polynomial can be classified by the number of its terms.

1 Term – Monomial

2 Terms – Binomial

3 Terms – Trinomial

– 2x3

– 6x + 9

– x2 – 4x + 7

A coefficient is a number that the variable is multiplied by.

Coefficient of 7x is 7

Coefficient of – 3y is – 3

Coefficient of x2 is 1 x2 = 1x2

Some polynomials have like terms that can be combined.

Remember, like terms contain the same variables raised to the same powers.

To combine like terms, combine the coefficients and keep the same variables and powers.

Combine like terms

– 3x + 8 – 2x – 5

= – 5x + 3

7x2 + 2x + x2 – 9x = 8x2 – 7x

6x2 + 2 + x2 – 9x + 4 = 7x2 – 9x + 6

The degree of a term is the sum of the exponents of the variables.

The degree of a polynomial is the highest degree of its terms

Find the degree of the following terms.

– 3x2

Degree = 2

8x3y6

Degree = 9

2x4y

Degree = 5

Find the degree of the following polynomials.

6

Degree = 0

4x2 – 3x + 1

Degree = 2

2x2 + 7x3 + x

Degree = 3

5x + 6

Degree = 1

Try This:

Classify each polynomial and find its degree.

8x4 – Monomial – Degree = 4

6x – 9 – Binomial – Degree = 1

x2 + 3x – 7 – Trinomial – Degree = 2

Combine like terms.

4x – 2 + 7 – x = 3x + 5

– 2x2 + 3 – 4x + 8x = – 2x2 + 4x + 3