1
Section 3.1  Polynomials
A
polynomial
is an expression made up of terms called monomials.
A
monomial
is an expression made up of one realnumber coefficient and (at least) one variable to some
wholenumber
power.
Examples are
3;
7
x
;
9
x
2
y
3
z
5
.
A polynomial made up of two monomials added to or subtracted from each other is called a
binomial
.
Examples:
3
xy
+ 6
z
2
;
2
x
– 8
x
3
;
4
abc
2
–
ab
3
.
A polynomial made up of three monomials added to or subtracted from each other is called a
trinomial
.
Examples:
4
abc
2
–
ab
2
+ 5
c
;
3
x
2
+ 9
x
6
– 6.
(Generally we do not name polynomials with four or more terms.)
Usually, polynomials that use only one variable are written with the highest exponent first and then in
descending order of exponents:
f
(
x
) =
a
n
x
n
+
a
n
1
x
n
1
+ .
.. +
a
1
x
+
a
0
The
degree of a monomial
is the sum of the powers of the variables.
Do not use the coefficient when
determining the degree.
Examples:
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 Spring '08
 Staff
 Polynomials

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