How do you use the remainder theorem to find the remainder for the division $(x^4+5x^3-14x^2)div(x-2)$ ?

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Answer 1 · 2016-09-08T14:37:50

$f(2) = 0$ There is no remainder.
$x-2$ is a factor.

If we have $f(x) = x^4 +5x^3-14x^2$

Let $x-2 = 0 rarr x =2$

The remainder of $x^4 +5x^3-14x^2 div(x-2)$
is found from $f(2)$

$f(2) = 2^4 +5(2)^3-14(2)^2$

= $16+40-56 =0$

The fact that the remainder is 0, (ie there is no remainder), means that $(x-2)$ is a factor of $x^4 +5x^3-14x^2$

How do you use the remainder theorem to find the remainder for the division (x^4+5x^3-14x^2)div(x-2)(x^4+5x^3-14x^2)div(x-2)?