HSA-REI.B.4.b — Solve Quadratics by Factoring

What HSA-REI.B.4.b Covers

High School, Algebra, Reasoning with Equations & Inequalities, Cluster B (solve equations and inequalities in one variable). The full standard lists five methods for solving quadratic equations: inspection, taking square roots, completing the square, the quadratic formula, and factoring — choosing whichever fits the equation's form. This page covers the factoring method only, on equations that factor cleanly into two integer binomials. It does not cover inspection, square roots, completing the square, the quadratic formula, or the complex-number solutions the full standard also asks students to recognize.

Where It Fits

Builds on Grade 8's 8.EE.C.7.b (linear equations with variables on both sides) and the factoring skill in HSA-SSE.B.3.a. Leads into graphing quadratic functions and identifying x-intercepts, and into the other four solving methods (square roots, completing the square, the quadratic formula) for equations that don't factor over the integers.

Common Mistakes

• Forgetting to set the equation equal to zero before factoring.
• Writing only one root when the factors give two distinct solutions.
• Sign errors when the constant term is negative (e.g., choosing +3 and +2 instead of −3 and +5 for a product of −6 and sum of +2).