Question 44393
f(x)=x^5+x^4-2x^3-x^2-x+2 i have to find all real and imaginary zero's, and can you explain the multiplicity of the real zero's for me,thanks

Since the coefficients add up to zero one of the zeroes is x=1.
Using synthetic division you can find the remaining factor is 
x^4+2x^3 -x-2.
The coefficients of this also add up to zero so x=1 is a zero again.
That is called multiplicity two because x=1 is a zero twice.
Again using synthetic division you can find the remaining factor is
x^3+3x^2+3x+2.
x=-2 is a zero for this. (I got this by graphing it.)
Synthetic says the quotient is x^2+x+1 which has complex zeroes.

Hope this helps.
Cheers,
Stan H.