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Multiplying Polynomials Calculator

The polynomial multiplication calculator is here to find the product of two one-variable polynomials of 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.