# How do you use the remainder theorem to find the remainder for the division (y^3+y^2-10)div(y+3)?

May 6, 2017

$- 28.$

#### Explanation:

As per the Remainder Theorem, when a poly. $P \left(y\right)$ is divided by

$\left(y - \alpha\right) ,$ the remainder is $P \left(\alpha\right) .$

Therefore, in our case, with, $P \left(y\right) = {y}^{3} + {y}^{2} - 10 ,$ we have,

$\text{The Remainder=} P \left(- 3\right) ,$

$= {\left(- 3\right)}^{3} + {\left(- 3\right)}^{2} - 10 ,$

$= - 27 + 9 - 10 ,$

$= - 28.$