When the polynomial x³ + 3x² - x + 2 is divided by x - 2, what is the remainder?

By the remainder theorem, dividing a polynomial $p(x)$ by $x - 2$ leaves the remainder $p(2)$. Compute $p(2) = 2^3 + 3(2)^2 - 2 + 2 = 8 + 12 - 2 + 2 = 20$, choice D. Synthetic division with coefficients 1, 3, $-1$, 2 gives 1, 5, 9, 20, confirming the remainder. Choice A (2) is the root value used for the divisor. Choice B (14) comes from a sign slip in the last term, $8 + 12 - 2 - 4$. Choice C ($-20$) has the wrong sign and does not match $p(2)$. Evaluate at the root of $x - 2$, namely $+2$.