The reflex that lets you check a factorization

You just factored an expression and you're not sure about the result. Instead of second-guessing yourself, expand your answer back out — checking is always faster than factoring itself.

If you factored x² + 5x + 6 into (x + 2)(x + 3), expand it back: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6. That matches the original expression exactly — your factorization is correct.

This reflex works for every type of factorization: common factor, difference of squares, trinomials. Expanding is a mechanical operation, far less error-prone than factoring.

Make this check a habit, especially on exams. It takes 20 seconds and completely removes the doubt.