SOLUTION: Given a polynomail and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials. X^3+2X^2-33X-90 ; X+5

Question 595715: Given a polynomail and one of its factors, find the remaining factors of the polynomial. Some factors may not be binomials.
X^3+2X^2-33X-90 ; X+5
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

To find the other factors we start by dividing by the known factor, x+5. I prefer synthetic division over long division:

-5 |   1   2   -33   -90
---       -5    15    90
     --------------------
       1  -3   -18     0

The remainder, in the lower right corner, is zero. This is to be expected when x+5 was supposed to be a factor. The other factor is found in the front of the remainder: 1 -3 -18. This translates into . Now we just factor that:

So your expression, fully factored, is:

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