Polynomial Multiplication Calculator

Work out polynomial multiplication instantly with clear inputs, formula shown and shareable results.

About Polynomial Multiplication Calculator

Multiplying polynomials convolves their coefficient lists: every term of the first multiplies every term of the second, and like powers are collected. The degree of the product is the sum of the two degrees.

Formula

Polynomial product

cₖ = Σⱼ aⱼ · bₖ₋ⱼ, deg(AB) = deg A + deg B

Worked example

With the default values below, Polynomial Multiplication Calculator returns Product of 2x^3 - 5x^2 - 2x + 15. Change any input above and every figure here is recalculated in your browser.

Inputs used

First polynomial coefficients, highest power first: 2, 3
Second polynomial coefficients: 1, -4, 5

Results

Product: 2x^3 - 5x^2 - 2x + 15
Degree of the product: 3
Non-zero terms: 4
Product evaluated at x = 2: 7.000000

Step by step

1Values used
2Polynomial product
3Product= 2x^3 - 5x^2 - 2x + 15
4Degree of the product= 3
5Non-zero terms= 4
6Product evaluated at x = 2= 7.000000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Multiply (2x + 3) by (x² − 4x + 5).

2x³ − 5x² − 2x + 15.

How many multiplications are needed?

The direct method needs (m+1)(n+1) products; fast transforms do better for very large polynomials.