Mathwarehouse Logo

Degree of Polynomial

The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial. To find the degree all that you have to do is find the largest exponent in the polynomial. Note: Ignore coefficients -- coefficients have nothing to do with the degree of a polynomial.

Practice Problems

Practice Problems II

Problem 6

What is the degree of the polynomial $$ 7x^3 + 2x^8 +33$$?

The answer is 8. Be careful sometimes polynomials are not ordered from greatest exponent to least. Even though 7x3 is the first expression, its exponent does not have the greatest value.

$$ 7x^3 + 2x^{ \red 8} +33 $$

Problem 7

What is the degree of the following polynomial $$ 5x^8 + 2x^9 + 3x^{ 11 } + 2x $$?

Just use the 'formula' for finding the degree of a polynomial. ie -- look for the value of the largest exponent. The answer is 11. Remember ignore those coefficients.

$$ 5x^8 + 2x^9 + 3x^{\red {11}} + 2x $$

Problem 8

What is the degree of the polynomial $$ x^2 + x + 2^3 $$ ?

The answer is 2. Do NOT count any constants("constant" is just a fancy math word for 'number'). IE you do not count the '23' which is just another way of writing 8.

$$ x^{\red 2} + x + 2^3 $$

Back to Polynomials Home