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As per given by the question,
There are given that four point.
The point is,
Now,
From given point,
Then, the factor is,
Now, solve the above equation,
The factorial formd will be,
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,
Then, a=2.
Now,
The value of a is 2.
And,
The polynomial in the factored form is,
Hence, the value of a is 2 and the polynomial in the factored form is,