Algebra Worksheets

Practice and master algebra concepts with our helpful walkthroughs and downloadable practice worksheets from our team of elite math educators.

Degree of a Polynomial

By Nancy Andreski

The Degree of a Polynomial is the sum of the exponents in the term of the highest degree.

Why is this concept useful?

The Degree of a Polynomial will be the greatest number of solutions of the polynomial and the greatest number of times the polynomial will cross the x-axis.

Where does this concept fit into the curriculum?

Algebra 1

How We Use Degrees of Polynomials:

To find the Degree of a polynomial, add the exponents for each term. The term with the highest sum will determine the degree.

When solving or graphing polynomial equations, the Degree of the Polynomial will indicate the number of possible solutions and the number of times the graph may cross the x-axis. A line (y = 5x + 2) will cross the x-axis once and have one solution because it has a Degree of 1. A quadratic equation, such as

2x2+3x+12x^2 + 3x + 1
, may cross the x-axis zero, one or two times and have zero, one or two solutions.

Sample Math Problems

1. What degree is the following polynomial?

4x7+3x2+24x^{7} + 3x^{2} + 2

Solution:

The greatest degree is 7, so this is a Polynomial of Degree 7.

2. What degree is the following polynomial?

8x2+3x4+5x8x^{2} + 3x^{4} + 5x

Solution: The greatest degree is 4, so this is a Polynomial of Degree 4.

3. What degree is the following polynomial?

x2y9+5x4+3x^{2} y^{9} + 5x^{4} + 3

Solution: This is a Polynomial of degree 11 because the first term has two exponents that add together to make 11, which is the greatest degree.

4. How many possible times could the following Polynomial cross the x-axis?

x7 − x2 + 1x^{7} \ -\ x^{2} \ +\ 1

Solution: This polynomial may cross the x-axis up to 7 times because it is a Polynomial of Degree 7.

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Practice Math Problems

1. What degree is the following polynomial?

2x9+2x4+52x^{9} + 2x^{4} + 5

2. What degree is the following polynomial?

7x4+3x9+2x7x^{4} + 3x^{9} + 2x

3. What degree is the following polynomial?

3x6y3+7x2+33x^{6} y^{3} + 7x^{2} + 3

4. How many possible times could the following Polynomial cross the x-axis?

x4−x3+x−1x^{4} - x^{3} + x - 1

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