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
Polynomial Remainder Theorem, the remainder of a polynomial when divided by is such that . 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 . This leaves you with an equation with one unknown. Now just solve for k.