Remainder Theorem

The Remainder Theorem states that when a polynomial \(f(x)\) is divided by a binomial of the form \((x - a)\), the remainder of that division is equal to \(f(a)\). In other words, to find the remainder, you simply evaluate the polynomial at \(x = a\). This means if you want to know what’s left over after dividing the polynomial by \((x - a)\), you just plug \(a\) into the polynomial, saving time compared to traditional long division. It's a shortcut that links polynomial evaluation directly to division remainders.