(a)

The polynomial function is .

The leading coefficient () is and constant term is .

The possible rational zeros : 

.

Thus, the possible rational zeros of the polynomial are .

(b)

The polynomial function is .

The possible rational zeros of polynomial are .

Draw a coordinate plane.

Graph the polynomial function.

Graph of the polynomial function is : \ \

Observe the above graph :

The zeros are in the list of possible rational zeros.

(c)

The polynomial function is .

The possible rational zeros of polynomial are .

Determine that is a rational zero by using synthetic division.

\ \

Factor the resulting quadratic expression. \ \

The complete factorization of f(x) is .

Find the real zeros of the function by equating to zero.

Thus, the real zeros of the function are .

(a)

The possible rational zeros of the polynomial are .

(b)

Graph of the polynomial function is : \ \

The zeros are in the list of possible rational zeros.

(c) The real zeros of the function are .