Calculadora de Multiplicação de Polinômios
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
(a₁x + b₁)(a₂x² + b₂x + c₂) = …
About this calculator
This calculator multiplies two polynomials: a linear one (a₁x + b₁) and a quadratic one (a₂x² + b₂x + c₂). The result is a cubic polynomial with coefficients for x³, x², x, and the constant term. It is useful for students and professionals who need to quickly verify the product of simple polynomials, avoiding manual errors.
The calculation follows algebraic distribution: each term of the first polynomial multiplies each term of the second. The coefficient of x³ is a₁ * a₂; x² is a₁ * b₂ + b₁ * a₂; x is a₁ * c₂ + b₁ * b₂; and the constant term is b₁ * c₂. The calculator displays the numerical coefficients and the resulting formatted polynomial.
Use this calculator when you need to multiply degree-1 and degree-2 polynomials, for example, in algebra problems, physics, or engineering. It is ideal for checking homework, simplifying expressions, or preparing teaching materials. The tool accepts real coefficients, including decimals.
Be careful when entering coefficients: ensure the values are correct, especially if negative. The calculator does not handle polynomials of degrees other than those specified. For higher-degree polynomials, use more advanced tools. Verify that the result makes sense in the context of your problem.
Frequently asked questions
Does the calculator accept fractional coefficients?
Yes, it accepts decimal numbers, which includes fractions written as decimals. For example, 0.5 or -3.2.
What happens if I enter a polynomial of a different degree?
The calculator is designed only for a linear and a quadratic polynomial. Entering other degrees may produce incorrect results. Use a generic tool for other cases.
Can I use this calculator to multiply more than two polynomials?
No, it only multiplies the two specified polynomials. To multiply several, do the product step by step or use computer algebra software.
Does the result show all terms even if a coefficient is zero?
Yes, the resulting polynomial is displayed with all terms, including zero coefficients, to maintain the standard cubic form.
What is the practical use of this multiplication?
Multiplying polynomials appears in areas like area calculation, volumes, kinematics, and mathematical modeling. It helps simplify expressions and solve equations.