When the polynomial x³ + 4x² - 2x + 1 is divided by x - 1, what is the remainder?

By the remainder theorem, dividing by $x - 1$ leaves the remainder $p(1)$. Compute: $p(1) = 1^3 + 4(1)^2 - 2(1) + 1 = 1 + 4 - 2 + 1 = 4$, choice B. Synthetic division with coefficients 1, 4, $-2$, 1 gives 1, 5, 3, 4, with remainder 4. Choice A (1) is the constant term or the root. Choice C (3) is the last coefficient in the quotient, one step before the remainder. Choice D ($-4$) results from evaluating at $x = -1$, which would be the divisor $x + 1$. Evaluate at the value that makes the divisor zero.