# How do you find the remainder when x^3+8x^2+11x-20 is divided by x-5?

Sep 17, 2016

When ${x}^{3} + 8 {x}^{2} + 11 x - 20$ is divided by $\left(x - 5\right)$, the remainder is $360$

#### Explanation:

According remainder theorem, if a polynomial $f \left(x\right)$ is divided by a binomial of degree $1$ i.e. $\left(x - a\right)$, the remainder is $f \left(a\right)$.

Hence, when ${x}^{3} + 8 {x}^{2} + 11 x - 20$ is divided by $\left(x - 5\right)$, the remainder is

$f \left(5\right) = {5}^{3} + 8 \times {5}^{2} + 11 \times 5 - 20$

= $125 + 8 \times 25 + 55 - 20$

= $125 + 200 + 55 - 20$

= $360$