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Polynomials
A polynomial
is just a sum of power functions where the exponents are all nonnegative
whole numbers.
Ex:
2
31
412
( )
47
3
64
2.315
5
f x
x
x
x
x
=

+

+
The degree
of a polynomial is the biggest exponent.
In the example above,
deg
412
f
=
.
The number in front of the
x
with the biggest exponent is the leading coefficient
.
Above,
the leading coefficient is –2.315.
These two numbers, along with the variable, make up
the polynomial’s leading term
.
The leading term here is
412
2.315
x

.
The leading term
eventually dominates
the polynomial.
If you graph both a polynomial and its leading
coefficient in a big enough window, they look identical.
The degree and the leading coefficient tell you the end behavior
of your graph.
As the
name implies, the end behavior of the graph is whether the ends of your graph go up or
down.
If the leading coefficient is positive, the righthand endpoint points up.
If the
leading coefficient is negative, then the righthand
endpoint points down.
If the degree is even, both
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This note was uploaded on 05/18/2011 for the course MATH 270 taught by Professor Vakarietis during the Summer '08 term at University of Louisiana at Lafayette.
 Summer '08
 VAKARIETIS
 Polynomials, Exponents

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