(a)
\The polynomial function is .
The definition of real zeros :.
and
and
.
and
.
,
and
.
The real zeros of this polynomial function are ,
and
.
The definition of zeros of multiplicity :, the exponent of factor
is
.
At the zeros of multiplicity is
.
At the zeros of multiplicity is
.
At the zeros of multiplicity is
.
(b)
\Find -intercept substitute
in function.
The polynomial function is .
and
and
.
and
.
,
and
.
Graph crosses -axis at
,
,
.
(c)
\Rewrite the above equation as .
At ,
At ,
At ,
(d)
\The polynomial function is .
Degree of the polynomial function .
Maximum number of turning points is .
The maximum number of turning points are .
(e)
\The polynomial function is .
The polynomial function of degree is .
The function behaves like
for large values of
.
(a)
\At the zeros of multiplicity is
.
At the zeros of multiplicity is
.
At the zeros of multiplicity is
.
(b)
\Graph crosses -axis at
,
,
.
(c)
\Near :
,
Near :
.
Near :
.
(d)
\The maximum number of turning points are .
(e)
\The function behaves like
for large values of
.