The function is .

Identify Possible Rational Zeros:

It is not practical to test all possible zeros of a polynomial function using only synthetic substitution.

The Rational Zero Theorem can be used for finding the some possible zeros to test.

Because the leading coefficient is , the possible rational zeros are the intezer factors of the constant term .

Therefore, the possible rational zeros of are .

The function is .

Draw the coordinate plane.

Graph the function .

Graph :

Observe the graph:

The function does not intersect any point on the axis.

Therefore The graph does not have rational zeros.

does not have rational roots.