Calculadora do Método da Caixa (fatorar trinômio)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
m · n = a·c ; m + n = b
About this calculator
The Box Method Calculator is an online tool that factors trinomials of the form ax² + bx + c, where a, b, and c are real numbers and a ≠ 0. The box method, also known as the product-sum method, finds two numbers m and n such that m · n = a·c and m + n = b. The calculator automates this process, displaying the factors of the trinomial.
To use it, simply enter the coefficients a, b, and c in the provided fields and click calculate. The tool then computes the product a·c and searches for integer pairs that satisfy the product and sum conditions. When found, it displays the factorization in the form (a₁x + m)(a₂x + n) or similar, depending on the values. If no integer factors exist, it informs that the trinomial is not factorable by this method.
Use this calculator when you need to factor quadratic trinomials to solve equations, simplify algebraic expressions, or in high school and college math problems. It is helpful for students learning factorization, teachers preparing exercises, or professionals dealing with algebra daily. The box method is especially efficient for trinomials with a leading coefficient different from 1.
Cautions: ensure the coefficients are entered correctly, especially the signs. The calculator assumes a, b, and c are integers; for fractional coefficients, you may need to adjust them first. Remember that the box method only works for trinomials that can be factored with integers. If the calculator finds no factors, the trinomial may be prime or require other methods like completing the square.
Frequently asked questions
What if the calculator does not find factors?
If no integer factors are found, the trinomial may be prime (not factorable over integers) or require rational numbers. Try using the quadratic formula or completing the square.
Can I use decimal or fractional coefficients?
The calculator is designed for integer coefficients. If you have decimals or fractions, multiply the entire expression by a factor to make them integers before entering.
Does the box method work for any trinomial?
No, it only works for trinomials that can be factored with integers. For other cases, use the quadratic formula or other methods.
What is the difference between the box method and factoring by grouping?
The box method is a variation of grouping, but it organizes terms in a 2x2 grid to visualize factors. The result is the same.
What does it mean when the calculator shows 'Factors: (x + m)(x + n)'?
This indicates that the coefficient a is 1. The factorization is (x + m)(x + n), where m and n are the numbers found.