Question

What is the value of k if 2x^3-3x^2+kx-4 is divided by x-3 and gives a remainder of -7?

Answer 1

By the polynomial remainder theorem, the remainder upon dividing a polynomial $p(x)$ by $x-c$ is the same as the value of $p(c)$.

Here $p(x)=2x^3-3x^2+kx-4$ and $c=3$. We have

$p(3)=23+3k=-7\implies k=-10$