Calculadora de Fatoração de Trinômios
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
ax² + bx + c = a(x − r₁)(x − r₂)
About this calculator
This calculator factors quadratic trinomials of the form ax² + bx + c, where a, b and c are real numbers and a is nonzero. The process uses the real roots r₁ and r₂ of the quadratic equation, obtained via the quadratic formula, to rewrite the trinomial as a(x − r₁)(x − r₂). It is a useful tool for simplifying algebraic expressions and solving problems involving factoring.
To use it, enter the coefficients a, b and c in the corresponding fields. The calculator checks whether the discriminant (b² − 4ac) is nonnegative, ensuring the roots are real. If the discriminant is negative, the trinomial cannot be factored over the real numbers and an error message is shown. Otherwise, the roots are computed and the factored form is displayed.
This tool is ideal for algebra students, teachers and professionals who need to factor trinomials quickly. It is useful for math homework, exam preparation and everyday tasks involving quadratic expressions. Factoring simplifies calculations and helps find zeros of functions, solve equations and analyze graphs.
Caution: the calculator only works for trinomials with real roots. If the discriminant is negative, factoring is not possible over the real numbers. Also, check that the entered coefficients are correct, as typos can lead to incorrect results. Remember that the order of factors does not change the product, but the calculator always factors out a first.
Frequently asked questions
What if the discriminant is negative?
If the discriminant is negative, the trinomial has no real roots and cannot be factored over the real numbers. The calculator will display an error message.
Can I factor trinomials with fractional coefficients?
Yes, as long as you enter the coefficients as decimals or fractions. The calculator converts them to decimals and performs the calculation.
Does the calculator show the step-by-step factoring?
No, it only shows the final result. For step-by-step, you can use a quadratic equation calculator.
What does the 'a' outside the parentheses mean in the factored form?
The 'a' is the coefficient of the quadratic term. It is factored out so that the expression becomes a(x − r₁)(x − r₂), maintaining equivalence with the original trinomial.
Does factoring work for trinomials with a = 1?
Yes, if a = 1, the factored form will be (x − r₁)(x − r₂), since multiplying by 1 does not change the product.