Examples for

# Polynomials

Polynomials are mathematical expressions that contain a sum of powers of indeterminate variables multiplied by coefficients. A core concept in algebra, polynomials are used in calculus and throughout all areas of mathematics. Wolfram|Alpha can compute several interesting properties of polynomials including extrema, roots, alternate forms, symmetry and parity. Additionally, polynomials can be factored, expanded or divided.

### Polynomials

Examine polynomials and compute properties like domain and range, degree, roots, plots and discriminant.

#### Compute properties of a polynomial:

#### Compute properties of a polynomial in several variables:

#### Find the degree of a polynomial:

#### Compute the greatest common divisor of polynomials:

#### Compute a polynomial from zeros:

### Expansion

Expand polynomial expressions using FOIL and other methods.

#### Expand a polynomial:

### Solving Polynomial Equations

Find all real and complex solutions of univariate and multivariate polynomial equations.

#### Solve a polynomial equation:

#### Solve a system of polynomial equations:

#### Find candidate rational roots of a polynomial:

### Factorization

Factorize quadratics and higher-degree polynomials.

#### Factor a polynomial:

### Long Division

Divide a polynomial by another polynomial to find the quotient and remainder.

#### Perform polynomial long division:

### Polynomial Interpolation

Find a polynomial curve that passes through a list of points.

#### Interpolate a dataset with a polynomial:

### GO FURTHER

Step-by-Step Solutions for AlgebraAlgebra Web App### RELATED EXAMPLES

### Completing the Square

Simplify a polynomial by completing the square.

#### Complete a square:

### Sums & Products of Roots

Determine the sum or product of all roots (not necessarily distinct) of a polynomial.