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Adding and Subtracting Polynomials Calculator

The adding and subtracting polynomials calculator finds the sum or difference of two polynomials up to degree 6.

Coefficients, highest power first. "1, 3, 2" means x² + 3x + 2.
Clear
Resultx^3 + 2x^2 - x - 2
Degree3
First polynomialx^2 + 3x + 2degree 2
Second polynomialx - 1degree 1
Value at x = 10equals the sum of the coefficients
Value at x = 0-2the constant term

Working

Problem(x^2 + 3x + 2) × (x - 1)
Resultx^3 + 2x^2 - x - 2
Coefficients1, 2, -1, -2

The method

add, subtract or multiply polynomials

FOIL is just distribution

Multiplying two binomials — First, Outer, Inner, Last — is the special case of multiplying every term of one polynomial by every term of the other. For longer polynomials the mnemonic runs out, but the method does not: distribute fully, then collect like powers.

Degrees add under multiplication: a quadratic times a linear gives a cubic. Under addition the degree is just the larger of the two, unless the leading terms cancel.