Summe Addition & Integration
Free online math tool

Polynomial Calculator

Evaluate polynomials, perform polynomial arithmetic, and calculate derivatives and integrals. Enter an expression in x and get a simplified result with a clear explanation of the method.

Calculate a polynomial

Use standard notation, such as 3x^2 + 2x - 5.

Use x for the variable and ^ for powers. Parentheses are supported.
Required for addition, subtraction, multiplication and division.
Used when evaluating P(x).

What is a polynomial?

A polynomial is an algebraic expression made from constants and variables raised to nonnegative whole-number powers. Its terms are combined using addition, subtraction and multiplication. For example, 3x^2 + 2x - 5 is a quadratic polynomial.

The degree is the largest exponent with a nonzero coefficient. The coefficient of the highest-degree term is called the leading coefficient, while the term without x is the constant term.

How to use this polynomial calculator

  1. Choose an operation from the dropdown menu.
  2. Enter polynomial A. Use ^ to write powers.
  3. For arithmetic involving two polynomials, enter polynomial B.
  4. For evaluation, enter a numerical value for x.
  5. Select Calculate polynomial to display the result.

Adding and subtracting polynomials

Addition and subtraction combine like terms. Like terms have the same power of x, so their coefficients can be added or subtracted.

(3x² + 2x - 5) + (x² - 4x + 1) = 4x² - 2x - 4

For subtraction, change the signs of the terms in the second polynomial before combining the matching powers.

Multiplying polynomials

To multiply polynomials, multiply every term in the first expression by every term in the second expression, then combine like terms.

(x + 2)(x - 3) = x² - x - 6

Evaluating a polynomial

Evaluation means replacing x with a given number and calculating the result. If P(x) = 2x² - 3x + 1, then at x = 4:

P(4) = 2(4²) - 3(4) + 1 = 21

Differentiation and integration

Differentiation applies the power rule to each term. For a term axⁿ, multiply its coefficient by n and reduce its exponent by one. Integration increases the exponent by one and divides the coefficient by the new exponent, adding an arbitrary constant C.

Frequently asked questions

Can I enter parentheses?

Yes. Expressions such as (x+2)(x-3) are supported.

Can I use decimal and negative coefficients?

Yes. For example, -2.5x^2 + 3x - 1 is valid.

Can I divide two polynomials?

Yes. Polynomial long division returns a quotient and a remainder. Division by zero is not permitted. Within the expression parser, the slash operator is supported only when the divisor is a nonzero constant.

What are the limits of this calculator?

It supports one variable, x, nonnegative integer exponents up to 30, and expressions up to 1,000 characters. Division inside an entered expression must be by a nonzero constant.