ABOUT POLYNOMIALS
A
polynomial function
in one variable has the form
f(x) = a
n
x
n
+ a
n-1
x
n-1
+ a
n-2
x
n-2
+ … + a
2
x
2
+ a
1
x + a
0
where n is a whole number and a
n
, a
n-1
, a
n-2
… a
2
, a
1
, a
0
are real numbers.
Polynomial functions can be classified based on the number of terms they have:
Monomial
functions (one term):
f(x) = 2x
Binomial
functions (two terms): y = –8 + x
2
Trinomial
functions (three terms):
f(x) = 2x
2
+ x - 5
or, based on their degree:
First degree (
linear
):
f(x) = 2x – 1
Note that y = 1 is also a first degree polynomial. When we
determine the degree of a polynomial, we use the highest degree
of its terms. Note that the term “y” has degree 1.
Second degree (
quadratic
):
y = 3x
2
+ 2x -2
Third degree (
cubic
):
y = x
3
+ 1
Fourth degree (
quartic
):
f(x) = -2x
4
+ 3x
3
– 2x + 1
Fifth degree (
quintic
):
f(x) = x
5
+ 3
A polynomial can also be classified as an
odd-degree
or an
even-degree
polynomial based on its degree.
Odd-degree polynomial functions, like y = x
3
, have graphs that extend diagonally
across the quadrants. Even-degree polynomial functions, like y = x

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- Spring '16
- polynomial function