Question: factoring 3 order polynomial equation with maple

I notice that when I tried to factor the polynomial

x^3+x^2+2*x+1 I did not get the rational roots of the polynomial, then I tried using synthetic division to solve for the roots but I could not find a root. So I believe that the roots of the polynomial equation are complex numbers...

How could I use synthetic division to find the rational roots of this integral so that I could do a Partial Fraction Decomposition for the integral...

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