Question

if k is a constant, determine and state the value of kids such that the polynomial k^2x^3-6kx+9 divisible by x-1

Answer 1

By the polynomial remainder theorem, $k^2x^3-6kx+9$ will be divisible by $x-1$ if the value of the polynomial at $x=1$ is 0.

$k^2(1)^3-6k(1)+9=k^2-6k+9=(k-3)^2=0$

which occurs for $k=3$.