Factoring Trinomials Calculator
How It Works
This factoring trinomials calculator uses established formulas to provide accurate results.
The basic rule:
- ax² + bx + c = a(x - r₁)(x - r₂)
- Discriminant: b² - 4ac
- Roots: x = (-b ± √(b²-4ac)) / 2a
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
How do I factor a trinomial?
For ax² + bx + c: find two numbers that multiply to a·c and add to b. Rewrite the middle term, then factor by grouping. Alternatively, use the quadratic formula to find roots r₁ and r₂, then write a(x - r₁)(x - r₂).
What if the trinomial cannot be factored?
If the discriminant b² - 4ac is negative, the trinomial has no real roots and cannot be factored over the real numbers. It can only be factored using complex numbers.
What is the AC method?
For ax² + bx + c, multiply a·c. Find two numbers that multiply to a·c and add to b. Split the middle term using these numbers, then factor by grouping. This always works when integer factors exist.
How do I check my factoring?
Multiply your factored form back out using FOIL (for binomials) to confirm you get the original trinomial.