2x^{3} + 5x^{2} – 8x + 1 y^{2} - 7y
+ 6 4z + 3 = 0

are examples of polynomials.

A polynomial function
is a function whose terms each consist of constant multiplied
by a power of a variable, such as 7y, 4z and 2x^{3}

For example, x^{2} - 4x + 7 is a polynomial, but x^{2}
- 4/x + 7x^{3/2} is not, because its second term involves
division by a variable, and also because its third term contains
an exponent that is not an integer.

Polynomials are one of
the most important concepts in algebra and throughout mathematics
and science. Polynomials are used to construct polynomial
rings, one of the most powerful concepts in algebra and algebraic
geometry.