Last updated October 6, 2026 · Report an error
Factoring a trinomial ax²+bx+c into two binomials comes down to finding the right pair of numbers to split the middle term — the classic "ac-method". This tool finds that pair automatically and factors by grouping.
How it works
It searches for two integers whose product equals a×c and whose sum equals b. Once found, the middle term bx is split using those two numbers, and the resulting four-term expression is factored by grouping into two binomials.
- Enter a (coefficient of x²).
- Enter b (coefficient of x).
- Enter c (constant).
- Click Calculate to see your results.
Examples
A factorable trinomial
2x²+7x+3: a×c=6, and 1+6=7, so it splits into 2x²+x+6x+3, which groups to (2x+1)(x+3).
A trinomial that doesn't factor
x²+x+1 has no integer pair multiplying to 1 and adding to 1, so it doesn't factor over the integers.
Who should use it
- Algebra coursework on factoring trinomials.
- Checking factoring homework before a test.
Industry applications
- Mathematics education
Advantages
- Systematically searches for the correct ac-method pair rather than relying on guesswork.
- Clearly reports when a trinomial has no integer factorization.
Limitations
- Limited to integer coefficients within a moderate range for a fast, reliable search.
Common mistakes to avoid
- Trying random factor pairs by trial and error instead of systematically checking factors of a×c.
Best practices
- Check the discriminant (b²-4ac) first — if it isn't a perfect square, the trinomial won't factor over the integers no matter what pair you try.
Tips
- If a=1, the ac-method simplifies to just finding two numbers that multiply to c and add to b — no splitting or grouping needed.
Frequently asked questions
It means no pair of whole numbers satisfies the ac-method conditions — the trinomial may still factor using irrational or complex numbers, just not with integer coefficients.
They solve the exact same underlying question (two numbers with a given product and sum) — the Diamond Problem calculator is a standalone version of this tool's first step.