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.