The question is as follows:

Given $\displaystyle x^3-4x^2+2x+1=0$

A. How many possible positive roots are there?

B. How many possible negative roots are there?

C. What are the possible rational roots?

D. Using synthetic substitution, which of the possible rational roots is actually a root of the equation?

E. Find the irrational roots of the equation.(Use the quadratic formula to solve the depressed equation.

My answers.

A. 1

B. 1

C.$\displaystyle \frac{1}{1}, -\frac{1}{1}$

D. Through application of synthetic substitution I determined that 1 is the only rational root.

E. This is where I have problems...

How do I derive this depressed equation? I remember reading that the product of synthetic substitution is a depressed equation. But I'm coming up with strange answers. Where am I going wrong?

I can provide working on request, but it is quite time consuming to do on my evo so I won't put it up immediately.

Thank you!