As per given by the question,
There are given that four point.
The point is,
[tex](-2,\text{ 0), (-1, 0), (0, -8), (2, 0)}[/tex]Now,
From given point,
[tex](-2,\text{ 0), (-1, 0), (0, -8), (2, 0)}[/tex]Then, the factor is,
[tex](x+2)(x+1)(x-2)[/tex]Now, solve the above equation,
[tex](x+2)(x+1)(x-2)[/tex]The factorial formd will be,
[tex]y=a\times(x+2)\times(x+1)\times(x-2)[/tex]Now, find the value of "a" with the help of given point (0, -8).
So,
Puth the value of x =0, and y=-8 in above equation,
Then,
[tex]\begin{gathered} y=a\times(x+2)\times(x+1)\times(x-2) \\ -8=a\times(0+2)\times(0+1)\times(0-2) \\ -8=a(2)(1)(-2) \\ a=\frac{-8}{-4} \end{gathered}[/tex]Then, a=2.
Now,
The value of a is 2.
And,
The polynomial in the factored form is,
[tex]y=2(x+2)(x+1)(x-2)[/tex]Hence, the value of a is 2 and the polynomial in the factored form is,
[tex]y=2(x+2)(x+1)(x-2)_{}[/tex]