Polynomial Calculator: Multiply, Roots
This polynomial calculator works with expressions in x such as 3x^2 - 2x + 1 or (x + 1)(x - 2)^2. Add, subtract, multiply or divide two polynomials with a quotient and remainder, expand a product into standard form, find the derivative or the integral, evaluate the polynomial at any x, and find all of its roots, including complex ones. Parentheses, powers, implicit multiplication like 2x(x + 3) and decimals are supported. The answer is written in standard form with the highest power first.
Polynomial Calculator
Add, subtract, multiply and divide polynomials, find roots, derivatives and integrals, or evaluate at x. Free online with steps.
How to use the Polynomial Calculator
- Type polynomial A, for example x^2 - 3x + 2. Powers use ^ and multiplication can be implied, as in 2x(x+1).
- Pick an operation. Add, subtract, multiply and divide also use polynomial B.
- For Evaluate, enter the value of x.
- Read the result, the degree and any roots, then copy it.
Features
- Add, subtract, multiply and divide with remainder
- Expands products and powers like (x+1)^3
- Derivative and integral
- Evaluate at any x using Horner's method
- All real and complex roots up to degree 30
- Standard form output with highest power first
Frequently asked questions
How do I multiply two polynomials?
Type one in A, the other in B and choose Multiply. Each term of A is multiplied by each term of B and like terms are combined. For example (x + 1)(x - 1) gives x^2 - 1.
How does polynomial long division work here?
Choose Divide. The calculator divides A by B and shows the quotient and the remainder, so that A = B × quotient + remainder and the remainder has a lower degree than B.
How are the roots found?
The calculator solves for every root numerically with the Durand-Kerner method, so a polynomial of degree n returns n roots, counted with multiplicity. Complex roots are shown as a + bi.
What input format can I use?
Use x as the variable, ^ for powers, + - * for operations and parentheses for grouping. Implied multiplication such as 3x or 2(x+1) works. You can also type x² or x³.
Why is an integral shown with fractions?
The integral of x^n is x^(n+1)/(n+1), so the coefficients are often fractions. They are shown as exact fractions when possible, followed by + C for the constant.