Students factor out the greatest common monomial factor from integer-coefficient binomials and trinomials and use grouping to reveal common binomial factors in standard low-degree polynomial expressions. They recognize and apply differences of squares, perfect-square trinomials, monic quadratic trinomials, and quadratic trinomials with non-unit integer leading coefficients, including appropriate sign choices. They select an efficient factoring strategy, factor expressions completely when possible, and verify equivalent factored forms by multiplication to support simplifying rational expressions and solving polynomial equations.