# Degree of a polynomial

The degree of a polynomial is a very straightforward concept that is really not hard to understand

Definition: The degree is the term with the greatest exponent

Recall that for y2, y is the base and 2 is the exponent

Example #1:

4x2 + 6x + 5

This polynomial has three terms. The first one is 4x2, the second is 6x, and the third is 5

The exponent of the first term is 2

The exponent of the second term is 1 because 6x = 6x1

The exponent of the third term is 0 because 5 = 5x0

What? 5x0 = 5?

Well, anything with an exponent of 0 is always equal to 1

Thus, 5x0 = 5 × x0 = 5 × 1 = 5

Since the highest exponent is 2, the degree of 4x2 + 6x + 5 is 2

Example #2:

2y6 + 1y5 + -3y4 + 7y3 + 9y2 + y + 6

This polynomial has seven terms. The first one is 2y2, the second is 1y5, the third is -3y4, the fourth is 7y3, the fifth is 9y2, the sixth is y, and the seventh is 6

The exponent of the first term is 6

The exponent of the second term is 5

The exponent of the third term is 4

The exponent of the fourth term is 3

The exponent of the fifth term is 2

The exponent of the sixth term is 1 because y = y1

The exponent of the last term is 0 because 6 = 6x0

Since the highest exponent is 6, the degree of 2y6 + 1y5 + -3y4 + 7y3 + 9y2 + y + 6 is 6

Write a polynomial for the following descriptions

1)

A binomial in z with a degree of 10

2)

A trinomial in c with a degree of 4

3)

A binomial in y with a degree of 1

4)

A monomial in b with a degree of 3

Anwers:

1)

2z10 − 4

2)

c4 + c2 − 8

3)

y + 4

4)

b3

To find the degree of a polynomial or monomial with more than one variable for the same term, just add the exponents for each variable to get the degree

Degree of x3y2. Degree of this monomial = 3 + 2 = 5

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