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

** a**_{n} x^{n} + a_{n-1} x^{n-1} + ... + a_{1} x + a_{0}

where the **coefficients** a_{k} are constant. If coefficient a_{n} is not equal to 0, then n (the highest power) is the **degree** of the polynomial and a_{n} is the **leading coefficient**.

Examples: These are polynomials.

1. -2 x^{3} + 4 x^{2} - 9 x + 12 , leading coefficient -2 and degree 3.

2. ( 1 /3) x^{5} - x^{3} - 9 x^{2} , 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

- x^{2} + 4 x - 9 and a x^{2} + b x^{2} + c

Answer: a = - 1 , b = 4 and c = -9

More references and links to polynomial functions.

Polynomial Functions