Precalculus · Problem 3.2.27

The Remainder Theorem tells you that when you divide a polynomial $p(x)$ by $(x - c)$, the remainder is simply $p(c)$—no division needed. Just substitute $c$ directly into the polynomial and evaluate. This is much faster than polynomial long division, and it immediately tells you whether $(x - c)$ is a factor (which happens exactly when $p(c) = 0$).

The Remainder Theorem tells you that when you divide a polynomial $p(x)$ by $(x - c)$, the remainder is simply $p(c)$—no division needed. Just substitute $c$ directly into the polynomial and evaluate. This is much faster than polynomial long division, and it immediately tells you whether $(x - c)$ is a factor (which happens exactly when $p(c) = 0$).