$\"\"$

The polynomial function is $\"\"$ .

Rewrite the function as $\"\"$ .

Find the intercepts :

Find $\"\"$ -intercepts by equating $\"\"$ to zero.

Rational zeros method :

Rational Root Theorem, if a rational number in simplest form $\"\"$ is a root of the polynomial equation $\"\"$ , then $\"\"$ is a factor of $\"\"$ and $\"\"$ is a factor if_{$\"\"$ .}

If $\"\"$ is a rational zero, then $\"\"$ is a factor of $\"\"$ and $\"\"$ is a factor of $\"\"$ .

The possible factors of $\"\"$ are $\"\"$ .

The possible factors for $\"\"$ are $\"\"$ .

So, $\"\"$ .

Consider $\"\"$ .

Using synthetic division :

$\"\"$

Therefore by factor theorem, $\"\"$ .

$\"\"$

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

The $\"\"$ -intercepts are $\"\"$ .

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

$\"\"$

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

$\"\"$

Construct a table to find the ordered pairs.

Choose different values of $\"\"$ and find corresponding $\"\"$ values.

\ \

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

\ $\"\"$ \	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$

$\"\"$

(1). Draw a coordinate plane.

(2). Plot the intercepts.

(3). Plot the points obtained in the above table.

(4). Connect those points with a smooth curve.

Graph :

$\"\"$ .

$\"\"$

Graph of the polynomial function $\"\"$ :

Graph :

$\"\"$ .