Convert quadratic trinomials ax² + bx + c into binomial factors. Includes roots and discriminant analysis.
Last updated: May 2026 | By Patchworkr Team
| Trinomial | Factored |
|---|---|
| x² + 5x + 6 | (x + 2)(x + 3) |
| x² - 7x + 12 | (x - 3)(x - 4) |
| 2x² + 5x + 3 | (2x + 3)(x + 1) |
| x² - 4 | (x - 2)(x + 2) |
Factoring a trinomial means expressing it as a product of two binomials. For a quadratic trinomial $ax^2 + bx + c$, the goal is to find two binomials whose product equals the original expression.
Methods include grouping (AC method), using the quadratic formula to find roots, and pattern recognition for special forms like perfect square trinomials.
Factor x² + 7x + 12
Then it's irreducible over the integers. Use the quadratic formula to find non-integer roots.
b² - 4ac. If negative, roots are complex; if zero, there's one repeated root.
Find two numbers multiplying to ac and adding to b, then rewrite and factor by grouping.
When solving quadratic equations, simplifying expressions, or analyzing function behavior.
Yes: difference of squares (a²-b²), perfect trinomials ((a±b)²), and others.
This tool handles real coefficients; complex factoring requires different methods.
Then it's not a quadratic (trinomial); it becomes linear and is treated separately.
If r is a root of ax²+bx+c, then (x-r) is a factor.
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