Factoring Calculator
Factoring means writing an expression as a product. This calculator shows which method applies and why, then expands the result back to prove it is right.
How it works
How the Factoring Calculator works
the part a result on its own leaves out
What factoring is
Factoring reverses multiplication. Expanding turns (x + 2)(x + 3) into x² + 5x + 6; factoring turns it back. The point is not tidiness — a product equals zero only when one of its factors does, which is what makes factored form the fastest route to the roots of an equation.
How this calculator decides
It takes out the common factor first, then checks the discriminant b² − 4ac. If that is a perfect square the roots are rational and integer factors exist, so it builds them from the roots. If it is not a perfect square, no integer factorisation exists and the calculator says so rather than guessing.
Common mistakes
Common mistakes with factoring
the errors that actually show up, not every possible slip
Forgetting the common factor first
2x² + 10x + 12 factors as 2(x + 2)(x + 3). Jumping straight to the trinomial method gives factors that do not multiply back correctly.
Sign errors in the pair
For x² − 5x + 6 the pair is −2 and −3, not 2 and 3. When the constant is positive and the middle term negative, both numbers are negative.
Assuming everything factors
x² + x + 1 has no integer factorisation. That is a fact about the expression, not a failure to spot the trick.
Questions
Asked often enough to answer here
answers that change how you work
How do I check a factorisation?
Expand it. If multiplying the factors back does not give exactly what you started with, the factorisation is wrong. This calculator does that check before showing you an answer.
What if the discriminant is negative?
Then the expression has no real roots and cannot be written as a product of real linear factors. It is irreducible over the reals.
Can it factor cubics?
Not yet — it handles quadratics, linear expressions and whole numbers. For higher degrees, find one root first and divide it out.
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