Question

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

divisible by x-1?

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}`