The Polynomial Analyzer turns entered coefficients into the degree, end behavior, real and complex roots, a full factorization, and the graph, with every step shown.
Type the coefficients from the highest power down to the constant. The analyzer finds every root, real or complex, and builds the factored form.
The degree is the highest power with a non-zero coefficient, and it caps the number of roots. The leading coefficient and the degree together set the end behavior: an even degree sends both ends the same way, an odd degree sends them in opposite directions.
For degree 3 and above there is no simple formula to use every time, so the analyzer uses the Durand–Kerner method, which refines all of the roots at once until they stop changing. It finds complex roots as well as real ones, so a degree-n polynomial always shows n roots, counted with repetition.
Each real root r gives a linear factor (x − r). Complex roots of a real polynomial come in conjugate pairs, and each pair multiplies back into one irreducible quadratic factor, so the result is the full factorization over the real numbers.