oddball wrote:When (x^3 - 2*x^2 + 2*k*x + 4) is divided by (x - 1), the remainder is 5. What is the value of k?

• (A) 0
  (B) 1
  (C) 2
  (D) 3
  (E) 4

This kind of problems can be solved with minimum calculation if we apply the polynomial remainder theorem. The theorem states that, if a polynomial p(x) is divided by (x - a) then the remainder is nothing but p(a). Let's see, how it is possible!

Say, p(x) = (x - a)*q(x) + r
Thus, when p(x) is divided by (x - a), the quotient is q(x) and remainder is r (which doesn't contain x).
Now, if we set x = a, p(a) = (a - a)*q(a) + r => r = p(a)

For more detailed discussion: https://www.purplemath.com/modules/remaindr.htm

Now, for this question: p(x) = (x^3 - 2*x^2 + 2*k*x + 4) => p(1) = (1 - 2 + 2k + 4) = (3 + 4k)
Therefore, (3 + 4k) = 5 => k = 1.

The correct answer is B.