# How do you use the remainder theorem to find the remainder when 2x^3 – x^2 – 3x + 7 is divided by x + 2?

Aug 22, 2015

The remainder is $- 7$

#### Explanation:

The Remainder Theorem tell us that when polynomial $P \left(x\right)$ is divided by $x - c$, the remainder is $P \left(c\right)$.

When P(x) = 2x^3 – x^2 – 3x + 7 is divided by $x + 2$,

we are dividing by $x - \left(- 2\right)$, so the remainder will be:

P(-2) = 2(-2)^3 – (-2)^2 – 3(-2) + 7

$= - 16 - 4 + 6 + 7 = - 20 + 13 = - 7$