Calculadora de Trinômio Quadrado Perfeito
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
b² = 4ac ⇔ (√a·x ± √c)²
About this calculator
The Perfect Square Trinomial Calculator checks whether a quadratic expression of the form ax² + bx + c is a perfect square trinomial. This tool is useful for students and professionals who need to factor quadratic expressions quickly and accurately, avoiding manual errors.
The operation is simple: the calculator applies the condition b² = 4ac. If true, the trinomial is a perfect square and the tool returns the factored form (√a·x ± √c)², where the sign matches that of b. Otherwise, it reports that it is not a perfect square trinomial.
Use this calculator when you need to factor expressions like 4x² + 12x + 9 or 9x² - 30x + 25, common in algebra problems, quadratic equations, and algebraic fraction simplification. It also helps verify exercise results.
Cautions: ensure that coefficients a and c are perfect squares (e.g., 1, 4, 9, 16) for valid factoring. Also, the calculator assumes standard form; negative coefficients require careful sign handling.
Frequently asked questions
What is a perfect square trinomial?
It is an expression of the form ax² + bx + c that can be written as (√a·x ± √c)², provided b² = 4ac.
Can I use the calculator with negative coefficients?
Yes, but pay attention to the sign of b. The calculator checks b² = 4ac, so the sign of b does not affect the condition, but the factored form will use the same sign as b.
What happens if a or c are not perfect squares?
The calculator still checks the condition b² = 4ac, but the square root may not be an integer. In that case, the expression may still be a perfect square with irrational coefficients.
How do I interpret the result (√a·x ± √c)²?
It means the original trinomial equals (√a·x + √c)² if b is positive, or (√a·x - √c)² if b is negative.
Does the calculator work with decimal coefficients?
Yes, it accepts decimals, but the condition b² = 4ac may lead to non-exact roots. The result will be displayed with approximation.