How this calculator works
Align terms by their exponent before combining coefficients. The lists may have different lengths; the shorter polynomial is padded at the highest powers. Subtraction changes every sign in Q. To find a missing input, rearrange the same polynomial equation rather than evaluating at a single x.
Formula
(P +/- Q)_j = P_j +/- Q_j. In P - Q = R, P = R + Q and Q = P - R.
Worked example
Add (x^2 + 2x + 3) and (2x - 3). Only like powers combine: x^2 stays unchanged, 2x + 2x = 4x, and 3 - 3 = 0. The answer is x^2 + 4x.
Advertisement
Frequently asked questions
How do I enter a missing power?
Use a zero in that position. The list 1, 0, -4 means x^2 - 4.
Are decimal coefficients accepted?
Yes. Coefficients are dimensionless real numbers; decimal arithmetic is approximate.
Does a leading zero change the answer?
No. Leading zeros are removed from the result without shifting the remaining powers.