How this calculator works
Each coefficient of the first polynomial multiplies every coefficient of the second. Products contributing to the same power are added. This coefficient convolution implements the distributive law without parsing algebraic text. Leading zeros are discarded; internal zeros preserve the power positions. Real decimal coefficients are evaluated with floating-point arithmetic.
Formula
If P(x) = sum a_i x^i and Q(x) = sum b_j x^j, their product has coefficient c_k = sum over i+j=k of a_i b_j.
Worked example
(x^2 + x + 1)(x - 1) expands to x^3 - x^2 + x^2 - x + x - 1 = x^3 - 1. For (2x^2 - 3)(x + 2), the product is 2x^3 + 4x^2 - 3x - 6.
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Frequently asked questions
How do I enter a constant?
Use a one-number list, such as 7. Its only coefficient is the constant term.
Why can the result degree drop?
Zero leading coefficients reduce the input degrees. Multiplying a zero polynomial gives the zero polynomial, whose degree is undefined.
Can I enter several variables?
No. A coefficient list represents a polynomial in one variable x only.