# How do you use the remainder theorem to determine the remainder when the polynomial x^3+3x^2-5x+2 is divided by x+2?

Sep 29, 2017

$16$

#### Explanation:

the remainder theorem states that if

$P \left(x\right) \text{ is divided by } \left(x - a\right)$

the remainder is$\text{ } P \left(a\right)$

so we have

$P \left(x\right) = {x}^{3} + 3 {x}^{2} - 5 x + 2 \text{ is divided by } x + 2$

so the remainder will be $P \left(- 2\right)$

$P \left(- 2\right) = {\left(- 2\right)}^{3} + 3 {\left(- 2\right)}^{2} - 5 \left(- 2\right) + 2$

$P \left(- 2\right) = - 8 + 12 + 10 + 2$

$P \left(- 2\right) = 16$