Introduction to Polynomials

A polynomial is an expression made up by adding and subtracting monomials.

Monomials

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 of Monomials

1.     2 x 2
2.     - 3 x
3.     (1 / 2) x 7

Binomials

We now define a binomial as a sum of 2 monomials that are not like.

Examples of Binomials

2 x + 8 , - x3 + 3 x , (1/2) x2 - x
A trinomial as a sum of 3 monomials that are not like.
Examples: 2 x3 + 8 x - 2 , 3 x4 - 5 x - 9 , 0.2 x2 - x + 4

Polynomials

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 of 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.

Equal Polynomials

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

Polynomial Functions