Question 727283
You literally perform long division on the polynomials.  Divide the {{{x^3-kx^2-6x+8}}}  by  {{{x+2}}}.  Watch each step extremely carefully.  In the last subtraction, if you did you algorithm correctly, you should have something equivalent to {{{8-2(2k-2)=12-4k}}}, and THIS MUST EQUAL ZERO, if the divisor, {{{x+2}}} is to be a binomial factor of the dividend cubic polynomial.  Set {{{12-4k=0}}} and find {{{k=3}}}.