POLYNOMIALS
Definition 1:
A
real polynomial
is an expression of the form
P
(
x
) =
a
n
x
n
+
a
n

1
x
n

1
+
· · ·
+
a
1
x
+
a
0
where
n
is a nonnegative integer and
a
0
, a
1
, . . ., a
n

1
, a
n
are real numbers with
a
n
= 0.
The nonnegative integer
n
is called the
degree
of
P
.
The numbers
a
0
, a
1
, . . ., a
n

1
, a
n
are called the
coefficients
of
P
;
a
n
is called the
leading coefficient
.
Examples:
•
Polynomials of degree
0:
The nonzero constants
P
(
x
)
≡
a
. Note:
P
(
x
)
≡
0
(the
zero polynomial) is a polynomial but no degree is assigned to it.
•
Polynomials of degree 1:
Linear polynomials
P
(
x
) =
ax
+
b
. The graph of a linear
polynomial is a straight line.
•
Polynomials of degree
2:
Quadratic polynomials
P
(
x
) =
ax
2
+
bx
+
c
. The graph
of a quadratic polynomial is a parabola which opens up if
a >
0, down if
a <
0.
•
Polynomials of degree
3:
Cubic polynomials
P
(
x
) =
ax
3
+
bx
2
+
cx
+
d
.
•
Polynomials of degree 4: Quartic polynomials
P
(
x
) =
a
4
x
4
+
a
3
x
3
+
a
2
x
2
+
a
1
x
+
a
0
.
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 Fall '08
 morgan
 Math, Polynomials, Real Numbers, Quadratic equation, Complex number

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