Add and Subtract Polynomials
Add and subtract polynomials by combining like terms with our free online calculator. Enter polynomial coefficients and get simplified results with step-by-step work.
About This Calculator
This calculator adds or subtracts two polynomials up to degree 2 by combining like terms. Enter the coefficients for the x^2, x, and constant terms of each polynomial, choose addition or subtraction, and get the simplified result instantly.
When adding, like terms are combined by adding their coefficients. When subtracting, the second polynomial is negated first (each coefficient sign is flipped), then like terms are combined.
Frequently Asked Questions
How do you add polynomials?
To add polynomials, combine like terms -- terms with the same variable raised to the same power. Add the coefficients of like terms while keeping the variable and exponent the same.
How do you subtract polynomials?
To subtract polynomials, distribute the negative sign to all terms of the second polynomial, then combine like terms. Change the sign of each term in the second polynomial before adding.
What are like terms in polynomials?
Like terms have the same variable raised to the same power. For example, 3x^2 and -5x^2 are like terms, but 3x^2 and 3x are not. Only the coefficients of like terms can be added or subtracted.
Can polynomials of different degrees be added?
Yes. When adding polynomials of different degrees, each polynomial contributes its own terms. Terms that don't have a match in the other polynomial simply carry over to the result unchanged.
What is the degree of a polynomial after addition?
The degree of the sum or difference is the highest exponent present in the result. If the leading terms cancel out, the degree may be lower than the original polynomials.
Is this tool free?
Yes, all calculators on Calculy are completely free to use with no registration required.