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`.