# How do you use the remainder theorem to evaluate f(a)=a^3+5a^2+10a+12 at a=-2?

##### 1 Answer
Oct 11, 2017

the remainder of the division $\left({a}^{3} + 5 {a}^{2} + 10 a + 12\right) : \left(a + 2\right)$ is 4

#### Explanation:

We simply will substitute $a = - 2$ in $f \left(a\right)$:

$f \left(- 2\right) = {\left(- 2\right)}^{3} + 5 {\left(- 2\right)}^{2} + 10 \left(- 2\right) + 12$

$= - 8 \cancel{+} 20 \cancel{- 20} + 12$

$= 4$

that means the remainder of the division:

$\left({a}^{3} + 5 {a}^{2} + 10 a + 12\right) : \left(a + 2\right)$

is 4