Trying to help my son out with a homework problem and not sure where I'm going awry. The question is What must be added to the polynomial f(x)= x^5 + x^4 + 3x^3 - 6x^2 - 4x + 8 so that the resulting polynomial is exactly divisible by g(x) = x - 2
The remainder theorem says that if f(x) is divided by g(x)=(x-a) then the remainder is f(a), correct? So in this case, a=2 and we want the remainder to be 0, correct? Thus we set f(2)+Z = 0 and solve for Z.
That leads me to 2^5 + 2^4 + (3)(2)^3 - (6)(2)^2 - (4)(2) + 8 + Z = 0
Which yields Z = -48.
However, this is a multiple choice question, and the choices are
Where have I gone wrong?