$\"\"$

The function is $\"\"$ .

Determine the end behavior of the graph of the function :

Expand the polynomial.

$\"\"$

The polynomial function $\"\"$ is of degree $\"\"$ .

The graph of $\"\"$ behave like $\"\"$ for large values of $\"\"$ .

Find the intercepts of the function:

$\"\"$ .

Find the $\"\"$ -intercepts by substituting $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ and $\"\"$ .

$\"\"$ -intercepts are $\"\"$ and $\"\"$ .

Find the $\"\"$ -intercepts by substituting $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$ -intercept is $\"\"$ .

Determine the zeros of the function and their multiplicity :

Use this information to determine whether the graph crosses or touches the $\"\"$ -axis at each $\"\"$ -intercept.

The zeros of the function are $\"\"$ and $\"\"$ .

The zero $\"\"$ is a zero of multiplicity $\"\"$ , so the graph of $\"\"$ crosses the $\"\"$ -axis at $\"\"$ .

Determine the maximum number of turning points on the graph of the function :

Degree of the function $\"\"$ is $\"\"$ .

Therefore, the number of turning points $\"\"$ .

At most $\"\"$ turning points.

Determine the behavior of the graph of $\"\"$ near each $\"\"$ -intercept :

Near $\"\"$ :

$\"\"$

$\"\"$ .

A line with slope $\"\"$ .

Near $\"\"$ :

$\"\"$

$\"\"$ .

A polynomial of degree $\"\"$ .

Put all the information from the steps 1 through step 5 together to obtain graph of $\"\"$ :

Plot the intercepts.

Construct a table of values to graph the general shape of the curve.

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\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Plot the points found in the above table and connect the plotted points.

Graph of the function $\"\"$ :

$\"\"$ .

Observe the graph of the function :

The function $\"\"$ in the interval $\"\"$ .

These values of $\"\"$ result in $\"\"$ .

From the graph, $\"\"$ , for $\"\"$ or $\"\"$ .

Thus, the solution set is $\"\"$ or in interval notation, $\"\"$ .

$\"\"$ ; $\"\"$ .