Polynomials play an important roles in mathematics and computer science. Ratios of polynomials can provide a good approximation to most functions with small errors and a reaonably small number of operations. These are called Padé approximants (see http://en.wikipedia.org/wiki/Pad%C3%A9_approximant).
A polynomials is a combination of coefficients (constant numbers) and variables (symbols standing for numbers) combined by using the usual arithmetic operations of addition, subtraction and multiplication.
When we multiply the same variable by itself multiple times, we replace a product of n instances of the same variable, x, with
xn = x * x * ... * x, n times
We say that the variable x has the exponent n, or that we have x to the power n. Assuming we are using numbers that are commutative under multiplication, then we assume that a polynomial is a sum of terms, each term being a product of a coefficient and variables to powers:
P(x1, x2, ..., xk ) = C0 + C1