Given that f(x)=x^3+kx^2–8x+2 and that when f(x) is divided by (x–k) the remainder is k, find the possible values of k assuming it is an integer.

Answer 1

If remainder when f(x) is divided by (x-k) is k, according to remainder theorem,

f(k)=k

:. f(k)=k^3+k(k^2)-8(k)+2=k

:. 2k^3-8k-k+2=0

:. 2k^3-9k+2=0

:. (k-2)(2k^2+4k-1)=0

:. k can be 2