The completely factored form of x^3 + 4x^2 - 9x -36 is
(x -3)(x + 3)(x + 4).
According to the given question.
We have a polynomial
x^3 + 4x^2 - 9x -36
Since for finding the roots of the above polynomial, first we randomly substitute any value of x and find for which value of x the above polynomial gives 0.
So, for x = 3
The above polymonial gets 0.
So, the one factor of the given polynomial is (x -3).
To find the other factors or completely factored form of the given polynomial we will divide x^3 + 4x^2 - 9x -36 by x - 3, which is called long division.
From the attatched solution or log division we can see that
The factored form of x^3 + 4x^2 - 9x -36 is (x -3)(x^2 + 7x + 12).
Now, the foctorization of x^2 + 7x + 12 is given by
x^2 + 7x + 12
= x^2 + 4x + 3x + 12
= x(x + 4) + 3(x + 4)
= (x + 3)(x + 4)
Therefore, the completely factored form of x^3 + 4x^2 - 9x -36 is
(x -3)(x + 3)(x + 4).
Find out more information about completely factored form here:
https://brainly.com/question/21850482
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