Here a few examples of polynomial functions:

f(x) = 4x^{3} + 8x^{2} + 2x + 3

g(x) = 2.4x^{5} + 3.2x^{2} + 7

h(x) = 3x^{2}

i(x) = 22.6

Polynomial functions are functions that have this form:

f(x) = a_{n}x^{n} + a_{n-1}x^{n-1} + ...
+ a_{1}x + a_{0}

The value of ** n **must be an

The ** coefficients**, as they are called,
are

The ** degree** of the polynomial function
is the highest value for

So, the degree of

g(x) = 2.4x^{5} + 3.2x^{2} + 7

is

5

Notice that the second to the last term in this form actually has x raised to an exponent of 1, as in:

f(x) = a_{n}x^{n} + a_{n-1}x^{n-1} + ... + a_{1}x^{1} + a_{0}

Of course, usually we do not show exponents of 1. So, we write a simple x
instead of x^{1}.

Notice that the last term in this form actually has x raised to an exponent of 0, as in:

f(x) = a_{n}x^{n} + a_{n-1}x^{n-1} + ... + a_{1}x + a_{0}x^{0}

Of course, x raised to a power of 0 is equal to 1, and we usually do not show multiplications by 1. So, the variable x does not appear in the last term.

So, in its most formal presentation, one could show the form of a polynomial function as:

f(x) = a_{n}x^{n} + a_{n-1}x^{n-1} + ... + a_{1}x^{1} + a_{0}x^{0}

Here are some polynomial functions; notice that the coefficients can be positive or negative real numbers.

f(x) = 2.4x^{5} + 1.7x^{2} - 5.6x + 8.1

f(x) = 4x^{3} + 5.6x

f(x) = 3.7x^{3} - 9.2x^{2} + 0.1x - 5.2