A student used synthetic division to divide x^3 - 3x^2 + 4. They got an answer of (x - 2) with a remainder of 2. Explain where they made errors in their work, then rewrite the equation with the correct steps. Then, using Remainder Theorem, is your answer and x + 1 a factor of the polynomial x^3 - 3x^2 + 4? If so, explain how you know. And then, if so, use the Factor Theorem to show the fully factored form of the polynomial x^3 - 3x^2 + 4.