HSA-SSE.B.3.a — Factor to Reveal Zeros

What HSA-SSE.B.3.a Covers

High School, Algebra, Seeing Structure in Expressions, Cluster B (write expressions in equivalent forms to solve problems). The standard asks students to factor a quadratic expression to reveal the zeros of the function it defines. Scope note: this generator presents each expression already set equal to zero (x² + bx + c = 0) so the zeros can be read off directly as x-values — the same factoring skill the standard asks for, applied to expressions that factor cleanly into two integer binomials.

Where It Fits

Uses the same factoring skill as HSA-REI.B.4.b (solving quadratic equations by factoring), but frames it as rewriting an expression to expose structure rather than solving an equation. Connects directly to graphing quadratic functions, where the zeros found here become the x-intercepts of the parabola.

Common Mistakes

• Reading the zeros as p and q instead of their opposites, −p and −q.
• Stopping at the factored form (x + p)(x + q) without stating the zeros as x-values.
• Missing a factor pair when the constant term has several possible integer factorizations.