SOLUTION: Factor the following polynomials completely making use of the given zero G(x)=x^3-(1-i)X^2-(8-i)x+(12-6i);2-i is a zero

Question 370375: Factor the following polynomials completely making use of the given zero
G(x)=x^3-(1-i)X^2-(8-i)x+(12-6i);2-i is a zero
Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!

If 2-i is a zero, then (x-(2-i)) or (x - 2 + i) is a factor of G(x). We need to find the other factor and for this we can use Synthetic Division:

2-i |   1  -1+i  -8+i  12-6i
-----       2-i   2-i -12+6i
       ----------------------
        1   1    -6     0

Te remainder is zero so 2-i is indeed a factor. And the rest of that row of numbers, 1 1 -6, tells us the other factor: . So now

The second factor is a trinomial that is easily factored giving:

G(x) is now fully factored.