Polynomials & Factoring — Core Skills

The core idea, one worked example, and short practice.

Written and reviewed by the Study Mondo Education TeamLast updated August 21, 2026

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Polynomials and Factoring: The Basics

A polynomial is an expression made of terms added or subtracted together, where each term is a number times a power of $x$ , like $4x^{3} - 2x^{2} + 7$ . The degree is the largest exponent, which is $3$ here. The leading coefficient is the number in front of that term, which is $4$ .

To factor means to rewrite something as a multiplication. Always start by pulling out the greatest common factor: the biggest number and the most $x$ letters that every term shares. For $6x^{2} + 15x$ , that is $3x$ , and the answer is $3x(2x + 5)$ .

After the common factor, check for a difference of squares, then use the two-number trick for $x^{2} + bx + c$ . Multiply back out to check. A zero comes from a factor: if $f(3) = 0$ , then $(x - 3)$ is a factor.

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