Factorize the following polynomial: $p(x) = x^{3} - 4x^{2} + 5x - 20$.

Which of the following groups matches the data of Part $I$ with the data of Part $II$?

Part $I$	Part $II$
$1.$ The graph of $p(x)=x^{2}-5x+6$	$a.$ Intersects the $X$-axis at one point.
$2.$ The graph of $p(x)=x^{2}-10x+25$	$b.$ Intersects the $X$-axis at zero points.
$3.$ The graph of $p(x)=x^{3}-4x$	$c.$ Intersects the $X$-axis at two points.
$4.$ The graph of $p(x)=x^{2}+4x+5$	$d.$ Intersects the $X$-axis at three points.

Identify the type of the following polynomial based on its degree: $p(x) = 7x^2 - 5x^3 + 3$.

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0)$ are $\alpha, \beta,$ and $\gamma,$ then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} = \dots$

Obtain the value of the following polynomial at the given value of $x$: $p(x) = x^{4} + 2x^{3} - x + 2$; at $x = 2$.

The number of real zeros of $y=p(x)$ is........... in the given figure.