Polynomial Addition Calculator

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

About Polynomial Addition Calculator

Polynomials add term by term: line the coefficients up by power and add. Missing powers count as zero, which is why the shorter list is padded on the left.

Formula

Polynomial addition

(Σaₖxᵏ) + (Σbₖxᵏ) = Σ(aₖ + bₖ)xᵏ

Worked example

With the default values below, Polynomial Addition Calculator returns Sum of 3x^3 + x^2 + 2x + 7. Change any input above and every figure here is recalculated in your browser.

Inputs used

First polynomial coefficients, highest power first: 3, 0, -2, 5
Second polynomial coefficients: 1, 4, 2

Results

Sum: 3x^3 + x^2 + 2x + 7
Difference (first minus second): 3x^3 - x^2 - 6x + 3
Degree of the sum: 3
Sum evaluated at x = 1: 13.000000

Step by step

1Values used
2Polynomial addition
3Sum= 3x^3 + x^2 + 2x + 7
4Difference (first minus second)= 3x^3 - x^2 - 6x + 3
5Degree of the sum= 3
6Sum evaluated at x = 1= 13.000000

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

Add 3x³ − 2x + 5 and x² + 4x + 2.

3x³ + x² + 2x + 7.

Why does the degree sometimes drop?

If the leading terms cancel, as in (x² + 1) + (−x² + 3), the degree falls — here to zero.