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(Section 1.7: Symmetry Revisited)
1.7.4
PART C: POLYNOMIAL FUNCTIONS
Short Cuts for Determining whether a Polynomial Function is
Even, Odd, or Neither
Let
fx
()
be a nontrivial (or “nonzero”) polynomial written in descending
powers of
x
, though the terms could be reordered.
• Delete any terms with zero coefficients.
• Nonzero constant terms have degree 0, which is an even degree.
•• We could rewrite the constant term 3, for example, as
3
x
0
.
•• We define
0
0
to be 1 here.
If every term of
has
even
degree, then
f
is
even
.
If every term of
has
odd
degree, then
f
is
odd
.
•
WARNING 1
:
If
has a nonzero constant term, then
f
can’t be odd.
If
has a term of even degree
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This document was uploaded on 12/29/2011.
 Spring '09

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