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

##### 1 Answer
Feb 21, 2017

$8$

#### Explanation:

The remainder theorem states that a polynomial $P \left(x\right)$ is divided by $\left(x - a\right)$ the remainder is $P \left(a\right)$

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

the remainder on dividing by $\left(x + 2\right) \text{ is } P \left(- 2\right)$

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

$P \left(- 2\right) = 2 \times - 8 + 3 \times 4 + 10 + 2$

$P \left(- 2\right) = - 16 + 12 + 10 + 2 = 8$