How to Use the Polynomial Factoring Calculator
The Polynomial Factoring Calculator factors a quadratic (ax²+bx+c) or cubic (ax³+bx²+cx+d) polynomial from its coefficients and shows the roots. For quadratics, it applies the quadratic formula directly based on the sign of the discriminant D=b²-4ac, giving real or complex roots. For cubics, it searches integers from -20 to 20 for a rational root using the rational root theorem, then uses synthetic division to reduce the remaining factor to a quadratic and factors that as well.
Choose the polynomial degree and enter the coefficients, and the factored form and roots appear instantly. If the leading coefficient a is 0, the tool explains that the expression isn't a valid polynomial of that degree. If the discriminant is negative, or no integer root is found for a cubic, the result explains the situation clearly. This is handy for checking factoring homework or studying for exams.
Frequently Asked Questions
It uses the rational root theorem to search integers from -20 to 20 for a root, then applies synthetic division to reduce the polynomial to a quadratic and factors that. If no integer root is found in this range, it reports that factoring isn’t possible.
The polynomial cannot be factored over the real numbers, and the calculator instead shows the complex roots (real part ± imaginary part i).
Yes, coefficients can be decimals as well as whole numbers.