# How do you use the remainder theorem to determine the remainder when the polynomial 8x^3+4x^2-19 is divided by x+2?

Dec 8, 2016

The remainder is $= - 67$

#### Explanation:

If we have a polynomial $f \left(x\right)$ and we divide by $\left(x - c\right)$

Then,

$f \left(x\right) = \left(x - c\right) q \left(x\right) + r \left(x\right)$

If $x = c$

We have, $f \left(c\right) = O + r$

$r$ is the remainder

That's the remainder theorem

Here, $f \left(x\right) = 8 {x}^{3} + 4 {x}^{2} - 19$

and $c = - 2$

So, $f \left(- 2\right) = - 8 \cdot 8 + 4 \cdot 4 - 19 = - 64 + 16 - 19 = - 67$