Polynomial Calculator

Solve polynomial equations, find roots, factor polynomials, and perform polynomial operations. Free online polynomial calculator.

Calculator

Polynomial Calculator

Solve polynomial equations, find roots, factor polynomials, and perform polynomial operations with our free online calculator. Supports polynomials of any degree.

Polynomial Calculator

Operation

Polynomial

Or Enter Coefficients:

Second Polynomial (for addition/multiplication)

Evaluation Point (x value)

Result

Enter polynomial above to see the calculation result.

Understanding Polynomials

Definition

A polynomial is an expression with variables and coefficients, using only addition, subtraction, multiplication, and non-negative integer exponents.

Degree

The degree is the highest power of the variable. For example, x³ + 2x² + 3x + 1 has degree 3.

Roots

Roots (zeros) are values of x that make the polynomial equal to zero. A polynomial of degree n has at most n roots.

Factoring

Factoring breaks a polynomial into a product of simpler polynomials, which helps find roots and simplify expressions.

How to Use

  1. Select the operation you want to perform
  2. Enter the polynomial in standard form or use coefficient inputs
  3. For binary operations, enter the second polynomial
  4. For evaluation, enter the x value
  5. Click "Calculate Polynomial Operation" to see the result
  6. Review the detailed solution and explanation

Examples

Solving Quadratic:

x² - 5x + 6 = 0 → x = 2, x = 3

Factoring:

x² - 4 = (x + 2)(x - 2)

Addition:

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

Evaluation:

f(x) = x² + 2x + 1, f(3) = 16

Features

  • • Solve polynomial equations
  • • Find roots and zeros
  • • Factor polynomials
  • • Add and multiply polynomials
  • • Evaluate at specific points
  • • Free to use

Perfect For

  • • Mathematics students
  • • Algebra homework
  • • Engineering calculations
  • • Physics problems
  • • Computer science
  • • Mathematical modeling

Frequently Asked Questions

What is a polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents.

How do I find the roots of a polynomial?

The roots (zeros) of a polynomial are the values of x that make the polynomial equal to zero. For quadratic polynomials, you can use the quadratic formula.

What is the degree of a polynomial?

The degree of a polynomial is the highest power of the variable in the polynomial. For example, x³ + 2x² + 3x + 1 has degree 3.