Finding k for Polynomial Roots

Consider the polynomial function:

$$ P(x) = 3x^4 - 8x^3 + kx^2 + 4x - 5 $$

for some constant $k$. If $P(x)$ has a root at $x = 2$, what is the value of $k$?

To find this value of $k$, you should substitute $2$ for $x$ in the polynomial and set the resulting expression equal to zero.