What is a polynomial?

A polynomial is a sum of terms with constant coefficients and nonnegative integer powers of variables. Division by a variable and fractional powers of a variable are not polynomial terms.

3x² − 2x + 7 is a polynomial. 1/x and √x are not polynomials in x.

Terms and degree

The degree of a polynomial in one variable is its highest power with a nonzero coefficient. A constant nonzero polynomial has degree zero.

  • Monomial: one term, such as 5x³.
  • Binomial: two terms, such as x + 4.
  • Trinomial: three terms, such as x² + 2x + 1.

Combine like terms

Terms with the same variables and powers can be added by adding their coefficients.

3x² + 2x + 4x² − x = 7x² + x.