We start by defining a monomial as a term of the form
a x n
where x is a variable, a is a constant and n is a nonnegative integer.
Examples: These are monomials.
1. 2 x 2
2. - 3 x
3. (1 / 2) x 7
We now define a binomial as a sum of 2 monomials and a trinomial as a sum of 3 monomials. A polynomial in x is the sum of any number of monomials and has the following form
an xn + an-1 xn-1 + ... + a1 x + a0
where the coefficients ak are constant. If coefficient an is not equal to 0, then n (the highest power) is the degree of the polynomial and an is the leading coefficient.
Examples: These are polynomials.
1. -2 x3 + 4 x2 - 9 x + 12 , leading coefficient -2 and degree 3.
2. ( 1 /3) x5 - x3 - 9 x2 , leading coefficient 1 / 3 and degree 5.
Two polynomials are equal if their corresponding coefficients are all equal.
Example: For what values of a, b and c are the polynomials
- x2 + 4 x - 9 and a x2 + b x2 + c
Answer: a = - 1 , b = 4 and c = -9
More references and links to polynomial functions.