(a)

The polynomial function is .

The definition of real zeros :.

and

and

and

The real zeros of this polynomial function are and .

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

At the zeros of multiplicity is .

At the zeros of multiplicity is .

(b)

Find -intercept substitute in the function.

The polynomial function is .

and

and

and

If the multiplicity of the function is odd then crosses the graph.

The graph touches the -axis at and crosses at  .

(c)

The polynomial function is .

The two -intercepts are and .

The factor gives rise to zero.

At ,

.

The factor gives rise to zero.

At ,

.

(d) 

The polynomial function is .

Degree of the polynomial function .

Maximum number of turning points is .

The maximum number of turning points are .

(e)

The polynomial function is .

The polynomial function of degree is .

The function behaves like for large values of .

(a)

The real zeros of this polynomial function are and .

At the zeros of multiplicity is .

At the zeros of multiplicity is .

(b)

The graph touches the -axis at and crosses at  .

(c)

Near : .

Near : .

(d)

The maximum number of turning points are .

(e)

The function behaves like for large values of .