I have not clue how to do it! can someone help me?
Use the Rational Zero Test to list all possible rational zeros of
f(x)=4x^5-8x^4-5x^3+10x^2+x-2
The rational root theorem tell you that all rational roots of a polynomial function with integer coefficients are of the form $\displaystyle a/b$ where $\displaystyle a$ is a factor of the constant term and $\displaystyle b$ a factor of the coefficient of the higest power of the variable.
So in this case the rational roots are among: $\displaystyle \{ a/b, a\in \{-2,-1,\ 1,\ 2\},\ b \in \{-4,-2,-1,\ 1,\ 2,\ 4\} \}$
or: $\displaystyle \{-2,\ -1,\ -1/2,\ -1/4,\ \ 1/4,\ \ 1/2,\ \ 1,\ \ 2 \}$
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