(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 .

is the zero of multiplicity is .

is the zero of multiplicity is .

(b)

Find -intercept substitute in the function.

The polynomial function is .

and

and

and

If the multiplicity of the function is even then touches the graph.

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

The graph touches the -axis at and 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 is .

Maximum number of turning points is .

The maximum number of turning points are .

(e)

The polynomial function is .

Rewrite the above function as

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 at .

(c)

Near : .

Near : .

(d)

The maximum number of turning points are .

(e)

The function behaves like for large values of .