# How do you use the remainder theorem to determine the remainder when 5w^3 – 2w + 10 is divided by w + 3?

Mar 23, 2016

Remainder is $- 119$

#### Explanation:

According to remainder theorem, if a polynomial $f \left(x\right)$ is divided by a $\left(x - a\right)$, then the remainder is given by $f \left(a\right)$.

Hence when $f \left(w\right) = 5 {w}^{3} - 2 w + 10$ is divided by $\left(w + 3\right)$, the remainder is given by $f \left(- 3\right)$

ie. $5 {\left(- 3\right)}^{3} - 2 \left(- 3\right) + 10$

= $5 \times \left(- 27\right) + 6 + 10$

= $- 135 + 16 = - 119$