# What is the degree of the polynomial 5x^5 + 8x^2 + 2x - 3x^9 - 8x^4 - 4x^5?

Nov 23, 2015

The degree will equal the value of the highest exponent(s) on a term .

#### Explanation:

This polynomial has a degree of 9 .

Note that $9$ is the highest exponent showing up on $- 3 {x}^{9}$

As another example, you can have several variables combined within a term, but it is the sum of the exponents that determines the highest degree:

$5 {x}^{10} - 3 {x}^{2} + 13 {x}^{6} {y}^{6} + 7$

Although $10$ appears to be the highest degree, do not be tricked! The correct degree for this polynomial is $12$, which is the sum of the exponents on $13 {x}^{6} {y}^{6}$

hope that helped