Factoring Trinomials Practice
An endless supply of never-repeating factoring problems with instant feedback. Hunt factor pairs, handle leading coefficients, remember GCF first — one problem at a time.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns another hint; a third miss walks you through the full solution.
2 What you’ll practice
Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.
x² + bx + c
The classic hunt: two numbers that multiply to c and add to b. All four sign patterns appear — positive, negative, and mixed.
ax² + bx + c
When the x² has a coefficient, the hunt gets fancier: match the First and Last products, then check the cross-terms.
GCF first and special cases
Always factor out the GCF before hunting. Plus difference of squares, perfect-square trinomials, and “prime” spotting.
3 Watch out for these
The three mistakes students make most often on these problems.
Wrong: x² − 7x + 12 = (x + 3)(x + 4) — FOIL gives +7x. Right: (x − 3)(x − 4). Decide the signs before hunting: c positive and b negative means both numbers are negative.
Wrong: 2x² + 10x + 12 = (2x + 4)(x + 3). Right: 2(x + 2)(x + 3) — GCF first, always.
Wrong: x² + x − 12 = (x + 6)(x − 2), unverified. Right: FOIL (x + 6)(x − 2) = x² + 4x − 12 ✗, so the answer is (x + 4)(x − 3). Check every hunt.