# How do you use the remainder theorem to find P(-3) for P(x) = x^3 + 3x^2 - x - 8?

It is $P \left(- 3\right) = - 5$

#### Explanation:

In order to find the value of $P \left(- 3\right)$ you need to divide the P(x) with $x + 3$ hence

$P \left(x\right) = {x}^{3} + 3 {x}^{2} - x - 8 = \left(x + 3\right) \cdot k \left(x\right) + q \left(x\right)$

or ${x}^{3} + 3 {x}^{2} - x - 8 = \left({x}^{2} - 1\right) \cdot \left(x + 3\right) - 5$

Hence the $P \left(- 3\right) = - 5$