Lecture 3: Section A.3
Polynomials and Factoring
Polynomials
Def.
A
polynomial in
x
is an expression of the
form
a
n
x
n
+
a
n
±
1
x
n
±
1
+
± ± ±
+
a
1
x
+
a
0
where
a
n
;
± ± ±
; a
0
are real numbers and
n
is a
nonnegative integer.
NOTE:
1)
a
n
;
± ± ±
; a
0
are the
coe±cients
of each term.
If
a
n
6
= 0, the polynomial has
degree
n
, and
a
n
is called
the
leading coe±cient.
2) Polynomials with one, two, and three terms are
called
monomials, binomials,
and
trinomials,
respectively.
3) In
standard form
, a polynomial is written with
descending powers of
x
.
4) A polynomial with all
a
i
= 0 (
i
= 0
;
1
;
± ± ±
:n
) is
called the
zero polynomial
. No degree is assigned
to the zero polynomial.
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State whether each is a polynomial.
For each
polynomial, rewrite it in standard form and ±nd its
degree.
1) 0
2)
±
2
3) 2
x
4
±
1 +
3
x
4) 2
x
5
+ 4
x
±
p
2
x
5) 5
x
±
7 +
p
3
x
8
±
4
x
5
Operations with Polynomials
1. Addition and Subtracttion
of Polynomials:
Combine like terms (same variable to the same powers)
by adding their coe²cients.
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 Spring '08
 WILLIAMSON
 Calculus, Algebra, Factoring Polynomials, Polynomials

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