# How do you find the remainder for (x^3+10x^2-4)div(x+10)?

Nov 26, 2016

The remainder is $= - 4$

#### Explanation:

Let $f \left(x\right) = {x}^{3} + 10 {x}^{2} - 4$

To find the remainder when $f \left(x\right)$ is divided by $\left(x - a\right)$

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

when $x = a$

$f \left(a\right) = \left(a - a\right) \cdot q \left(a\right) + r$

$f \left(a\right) = 0 + r = r$

Here, $f \left(x\right) = {x}^{3} + 10 {x}^{2} - 4$

and $a = - 10$

So, $f \left(- 10\right) = - 1000 + 1000 - 4 = - 4$