Step 1:

(a)

The polynomial function is .

The definition of real zeros :.

The real zeros of this polynomial function are .

The definition of zeros of multiplicity :, the exponent of factor is .

At the zeros of multiplicity is .

At the zeros of multiplicity is .

Step 2:

(b)

Find x-intercept substitute in function.

The polynomial function is .

The graph crosses or touches the x-axis at and .

Step 3:

(c)

The polynomial function is .

The two -intercepts are .

The factor gives rise to zero.

At ,

.

The factor gives rise to zero.

At ,

.

Step 4:

(d)

The polynomial function is .

Turning points are nothing but the local minimum / maximum .

To find the local minimum / maximum , equate the first derivative to zero .

Apply product rule of derivatives : .

Apply power rule of derivatives : .

The polynomial function is as a turning points at and

The maximum number of turning points are .

Step 5:

(e)

The polynomial function is .

The polynomial function of degree is .

This function behaves like for large values of .

Step 1:

(a)

The polynomial function is .

The definition of real zeros :.

The real zeros of this polynomial function are .

The definition of zeros of multiplicity :, the exponent of factor is .

At the zeros of multiplicity is .

At the zeros of multiplicity is .

Step 2:

(b)

Find x-intercept substitute in function.

The polynomial function is .

The graph crosses or touches the -axis at and .

Step 3:

(c)

The polynomial function is .

The two -intercepts are .

Near ,

.

Near ,

.

Step 4:

(d)

The polynomial function is .

Turning points are nothing but the local minimum or maximum .

To find the local minimum / maximum , equate the first derivative to zero .

Apply product rule of derivatives : .

Apply power rule of derivatives : .

The polynomial function is as a turning points at and

The maximum number of turning points are .

Step 5:

(e)

The polynomial function is .

The polynomial function of degree is .

This function behaves like for large values of .