Polynomial Calculator
Add, subtract, or multiply two polynomials (up to quadratics) and get the simplified result.
Combining like terms
Adding or subtracting polynomials works by combining 'like terms' — terms with the same power of x. The x² terms combine with each other, the x terms combine with each other, and the constants combine with each other, each independently of the other groups.
This is the same principle as combining units in everyday math — you can add 3 apples and 2 apples to get 5 apples, but you can't directly combine apples and oranges. Here, x² terms, x terms, and constants are the different 'units' being kept separate.
Why multiplication increases the degree
Multiplying two quadratics (degree 2) produces a degree 4 result, since multiplying x² by x² gives x⁴ — each term in the first polynomial must be multiplied by each term in the second, similar to multiplying two binomials with the FOIL method, just with more terms to track.
This calculator handles that full expansion and combines like terms automatically, which becomes tedious and error-prone to do by hand as the number of terms grows.
Frequently asked questions
Why can't I just add all the coefficients together?
Only terms with the same power of x can be combined — an x² term and an x term represent fundamentally different quantities, similar to how you can't directly combine different units of measurement.
Why does multiplying two quadratics give a degree-4 result?
Because multiplying the highest-degree terms (x² × x²) produces x⁴ — multiplication of polynomials adds their degrees together, so two degree-2 polynomials multiply to a degree-4 result.