Mastering the Remainder Theorem: Synthetic Division vs. Polynomial Long Division
Why the Remainder Theorem is the fastest shortcut on the SAT and calculus exams to factor high-degree polynomials without tedious long division. We break down the algebraic proof, synthetic table setups, and common negative sign traps.
P(x) = Q(x) · (x - c) + R ⟹ P(c) = R
Evaluating the remainder of P(x) ÷ (x - 2) is equivalent to finding P(2) in single-step evaluation.
Dr. Sarah Chen
Computational Mathematics, MIT
Remainder = -5 | Quotient = 2x² - x + 1
90% Faster: Avoids writing x², x, and variable placeholders across 6 vertical rows.
Companion Solver: Direct integration with SolveCalc's Polynomial Workbench.