The degree polynomial function and leading coefficient .

The polynomial function .

The degree of polynomial is even (n = 4) and leading coefficient is positive ().

Since the graph rises to the left and right.

The graph rises to the left and right.

To find the real zeros of the function, set f(x) equal to zero and solve for x.

The polynomial function .

                                   (Set f(x) equal to zero)

                               (Remove common monomial factor)

                     (Factor completely)

So, the real zeros are .

Since the x - intercepts occur at .

The real zeros are .

The polynomial function .

Make the table

Make the table

The factor , k > 1, yields a repeated zero x = a of multiplicity k.

If k is odd, the graph crosses the x - axis at x = a.

If k is even, the graph touches the x - axis ( but does not cross the x - axis ) at x = a.

The polynomial function .

The factor form of polynomial function .

The zeros of polynomial function are .

The exponent is greater than 1, the factor yields the repeated zero x = 0.

Since the zero of " g ", x = 0 is even multiplicity because k = 2.

So, the graph touches the x - axis ( but does not cross the x - axis ) at x = 0.

The remaining zero of " g " are and these are odd multiplicity because k = 1.

So, the graph crosses the x - axis at .

The polynomial function graph is