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.

Polynomials

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

Compute properties of a polynomial:

x^4 - 4x^3 + 8x + 1

Compute properties of a polynomial in several variables:

x^3 + x^2 y + x y^2 + y^3

Find the degree of a polynomial:

deg (x+2)^5-(x-2)^5

Compute the greatest common divisor of polynomials:

gcd x^4-9x^2-4x+12, x^3+5x^2+2x-8

Expansion

Expand polynomial expressions using FOIL and other methods.

Expand a polynomial:

expand (x^2 + 1)(x^2 - 1)(x+1)^3
expand (x + y + z)^10

Polynomial Interpolation

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

Interpolate a dataset with a polynomial:

interpolating polynomial {1,10},{2,3},{4,7},{8,0}
interpolating polynomial calculator

Factorization

Factorize quadratics and higher-degree polynomials.

Factor a polynomial:

factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48
factor x^12 - y^12

Completing the Square

Simplify a polynomial by completing the square.

Complete a square:

complete the square x^2+10x+28

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Step-by-Step Solutions for Algebra

Algebra Web App

RELATED EXAMPLES

  • Arithmetic
  • Derivatives
  • Domain & Range
  • Equation Solving
  • Integrals
  • Limits
  • Rational Functions
  • Simplification

    • Solving Polynomial Equations

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

    Solve a polynomial equation:

    x^3 - 4x^2 + 6x - 24 = 0

    Solve a system of polynomial equations:

    x^2+y^2=1, (x-2)^2+(y-1)^2=4

    Find candidate rational roots of a polynomial:

    rational solutions of x^3 - 3x + 2