SOLUTION: If(x+2) is one factor of 9x^3+10x^2-17x-2, use synthetic division to find all roots? I attempted to do it but, I am not able to find a answer that will work?

Question 28755: If(x+2) is one factor of 9x^3+10x^2-17x-2, use synthetic division to find all roots?
I attempted to do it but, I am not able to find a answer that will work?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If x+2 is a factor then x=-2 is a root.
Set up the synthetic 9 10 -17 -2 and use -2 as the root.
You get a quotient of 9x^2-8x-1
The sum of these coefficients is zero so x=1 is a root.
Set up the synthetic of 9 -8 -1 and use 1 as a root .
You get a quotient of 9x+1.
Set that equal to zero to get x=-1/9
The roots are -2,1,-1/9
Cheers,
Stan H.
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