Mathematics

The key insight is the Remainder Theorem: when you divide a polynomial by a linear divisor $(x - a)$, the remainder is simply the value of the polynomial evaluated at $x = a$. Instead of doing long division, you can skip straight to plugging in $x = 3$ into the original polynomial—that single number is your answer. This transforms a tedious calculation into a quick substitution.

The key insight is the Remainder Theorem: when you divide a polynomial by a linear divisor $(x - a)$, the remainder is simply the value of the polynomial evaluated at $x = a$. Instead of doing long division, you can skip straight to plugging in $x = 3$ into the original polynomial—that single number is your answer. This transforms a tedious calculation into a quick substitution.