How Factoring Works
Factoring means rewriting something as a product of simpler pieces. For integers, the “simplest pieces” are prime numbers; for quadratics, they are linear factors like (x + 2). Factoring is the reverse of expanding — and it is how you solve most equations you meet in algebra class.
Factoring Integers
Divide by the smallest primes first: 2, 3, 5, 7, … Each division is shown above until only primes remain. Writing the result with exponents (360 = 2³ × 3² × 5) makes the structure obvious and is essential for LCM/HCF work.
Factoring Quadratics
For x² + bx + c, hunt for two numbers with product c and sum b. For ax² + bx + c with a ≠ 1, the discriminant Δ = b² − 4ac decides everything: a perfect square means clean integer factors, a negative Δ means no real factorization at all.
Solving the factored equation? Try our quadratic equation solver or the algebra calculator.