Question

If k is a constant, what is the value of k such that the polynomial k^2x^3 - 6kz+9 is

Answer 1

$x-1$ divides $p(x)=k^2x^3-6kx+9$ if the remainder is $p(1)=0$. (This is the remainder theorem)

Then we must have

$p(1)=k^2-6k+9=(k-3)^2=0\implies\boxed{k=3}$