Polynomials Summary

Algebra 1 · Axiom Academy

A recap of Unit 6 — the vocabulary of polynomials, the four operations, the special products, and every factoring method we used to solve equations. A polynomial is a sum of terms, each a coefficient times a variable raised to a whole-number exponent; its degree is the highest exponent. Add and subtract by combining like terms ; multiply by distributing every term of one factor across the other. Two special products are worth memorizing: the square of a binomial (a+b)^2 and the difference of squares a^2-b^2 . Always factor out the GCF first , then reach for trinomial factoring, grouping, or the difference of squares. To solve, set the equation to zero, factor completely, and apply the Zero Product Property . Core Concept What Is a Polynomial? A polynomial is a sum of terms, where each term is a coefficient multiplied by a variable raised to a whole-number exponent. Written in standard form , the terms run in descending order of exponent. Degree: the highest exponent — it governs the polynomial's behavior. Examples: 3x^2 - 5x + 2 has degree 2; x^3 + 2x^2 - x + 7 has degree 3. Core Concept Polynomial Operations Add and subtract by combining like terms — terms with the same variable and exponent; the coefficients combine while the exponent stays put. Multiply by distributing each term of the first polynomial across every term of the second. When to use: an area model makes multiplication easy to visualize.

This is the written version of the interactive lesson above. See the full Algebra 1 course.