Add & Subtract Polynomials Calculator
Enter the coefficients of two polynomials (up to degree 3) and choose to add or subtract — get the result polynomial and a step-by-step breakdown of how each like term is combined.
Operation
First polynomial P(x)
Second polynomial Q(x)
Align like terms by degree (add coefficients)
Evaluate each bracket
Drop zero terms → R(x)
How does this calculator work?
To add or subtract polynomials, combine like terms by degree: (a₃±b₃)x³ + (a₂±b₂)x² + (a₁±b₁)x + (a₀±b₀). Terms that cancel to zero are dropped from the result. The degree of the output equals the highest remaining non-zero power.
Formula
How this is calculated
Polynomial addition and subtraction work term by term: only terms that share the same variable power — called like terms — can be combined. This calculator handles polynomials up to degree 3, treating each power (x³, x², x, and the constant) as a separate "column".
For each degree, the coefficient of the first polynomial is added to (or subtracted from) the coefficient of the second polynomial. For example, combining the x² terms of 3x² and −2x² gives (3 + (−2))x² = x². If the result for a given degree is zero, that term is dropped from the output — which may reduce the degree of the result below that of either input polynomial.
The calculator accepts any real (decimal) coefficients. The degree of the result is the highest power with a non-zero coefficient. If all coefficients cancel to zero, the result is the zero polynomial.
Frequently asked questions
Like terms are terms with exactly the same variable raised to the same exponent. In polynomials, 3x² and −x² are like terms because both involve x², while 3x² and 3x are not (different exponents). Only like terms can be combined — you cannot add an x² term to an x term.
Yes. If the leading terms cancel — for example 2x³ + (−2x³) = 0 — the degree of the result drops. In the extreme case of P(x) − P(x), every term cancels and you get the zero polynomial.
Just set the higher-degree coefficients to 0. The zero terms are hidden in the displayed result, giving a lower-degree polynomial. For example, a quadratic is entered as 0 for x³, then the x², x, and constant coefficients.
Also known as
TG we-Calculate Editorial Team. (2026). Add & Subtract Polynomials Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/add-subtract-polynomials-calculator
TG we-Calculate Editorial Team. "Add & Subtract Polynomials Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/add-subtract-polynomials-calculator.
TG we-Calculate Editorial Team, "Add & Subtract Polynomials Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/add-subtract-polynomials-calculator
@misc{wecalculate_add_subtract_polynomials_calculator, title = {Add & Subtract Polynomials Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/add-subtract-polynomials-calculator}}, year = {2026}, note = {TG we-Calculate} }
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