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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
X%5E3%2B2X%5E2-33X-90
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 x%5E2+-3x+-+18. Now we just factor that:
x%5E2-3x-18+=+%28x-6%29%28x%2B3%29

So your expression, fully factored, is:
X%5E3%2B2X%5E2-33X-90+=+%28x%2B5%29%28x-6%29%28x%2B3%29