# Math Help - Polynomial Long Division

1. ## Polynomial Long Division

Determine the value of K such that when:
f(x) = x^4 + kx^2 - 3x - 5
is divided by (x-1), the is remainder -10

2. Originally Posted by B-lap
Determine the value of K such that when:
f(x) = x^4 + kx^2 - 3x - 5
is divided by (x-1), the is remainder -10
k = -3

3. Originally Posted by dc52789
k = -3
Reason being, because of the Polynomial Remainder Theorem, the remainder $r$ of a polynomial $P(x)$ when divided by $(x-a)$ is such that $r = P(a)$. Proof of why this happens in the link. It's not definetely NOT complicated, but it's senseless to just glue it here.

As for your problem, it's a pretty much direct application. You want the remainder of that division to be -10, so $f(1) = 10$. This leaves you with an equation with one unknown. Now just solve for k.