Alright!
From what I understand, I will choose 2 factors which are the same so that it is the GCF.
What you can randomly do is choose 3 factors in the form (x-a)(bx-c)(x-a).
Say, I choose (x-3)(2x-1)(x-3).
Multiply them until you get the polynomial:
\[(2x ^{2}-x-6x+3)(x-3)=(2x ^{2}-7x+3)(x-3)=2x ^{3}-6x ^{2}-7x ^{2}+21x+3x-9\]
\[2x ^{3}-13x ^{2}+24x-9\]
Now this is one way of writing the polynomial.
The other way of writing it is by finding the factors of the polynomial.
To do so, we have to find the factors of the last value of the polynomial.
In this case is a 9
The factors are \[\pm1;\pm3;\pm9\] By trial, we plot one of the values into the polynomial to get a 0.
If we try with say +3, we get \[2(2)^{3}-13(3)^{2}+24(2)-9=0\] Therefore, this is a factor.
Now we know that one of the ways of writing the polynomial is (x-3).
To find the other part, we have to consider the degree of the maximum variable from the main polynomial, in this case is X^3.
Given that a factor is (x-3), it must multiply with a x^2 to give x^3. Plus, we have to consider the coefficient of such variable, which is 2.
So we get (x-3)(2x^2+tx+c)
To facilitate more, we find c, which is found by dividing the coefficient of the first factor from the last value of the original polynomial (-9). The calculation for C is then -9/-3= +3.
Our factors now become (x-3)(2x^2+tx+3)