# How do you find the degree of P(x) = x^3(x+2)(x-3)^2 ?

May 7, 2018

$P \left(x\right)$ has degree 6

#### Explanation:

$P \left(x\right) = {x}^{3} \left(x + 2\right) {\left(x - 3\right)}^{2}$

The degree of a polynomial is highest degree of its individual terms.

In this example we could expand $P \left(x\right)$ into its individual terms but in this case that is unnecessary.

Consider the highest degree of each of the factors of $P \left(x\right)$.

${x}^{3}$ has degree 3

$\left(x + 2\right)$ has highest degree 1

${\left(x - 3\right)}^{2}$ has highest degree 2

Hence the degree of $P \left(x\right) = 3 + 1 + 2 = 6$