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

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Answer 1 · 2016-04-28T23:12:36

The remainder theorem states the following:

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

$r = (-4)^4 + 2(-4)^2 + 5(-2) - 10$

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

$r = -224$

The remainder is -224

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