# How do you use the remainder theorem to determine the remainder when d^ 4 + 2d ^2 + 5d – 10 is divided by d + 4?

Apr 28, 2016

The remainder theorem states the following:

#### Explanation:

Consider the following division: ƒ(x) = (ax^3 + ax^2 + ax + a) ÷ (x - b), then the remainder will be given by evaluating ƒ(b)

$r = {\left(- 4\right)}^{4} + 2 {\left(- 4\right)}^{2} + 5 \left(- 2\right) - 10$

$r = - 256 + 32 - 10 - 10$

$r = - 224$

The remainder is -224