<s>[INST] Let $r,s,t$ be the roots of the equation $ x^3 - 6x^2 + 5x + 1$. What is the value of $(2-r)(2-s)(2-t)$? Let $r,s,t$ be the roots of the equation $ x^3 - 6x^2 + 5x + 1$. What is the value of $(2-r)(2-s)(2-t)$?
The question is mentioned in my math olympiad. Please explain how to solve the problem. I have factorised the equation to $$-x^2+1, x-6x, -5x +1.$$
I am only in year 6.
 [/INST] If $r,s,t$ be the roots of the equation $x^3 - 6x^2 + 5x + 1=0$, then $$x^3 - 6x^2 + 5x + 1 = (x - r)(x - s)(x - t)$$ 
Now, determine the value of $f(2)$ by evaluating $$x^3 - 6x^2 + 5x + 1\quad\text{at} \;x = 2\;\tag{$f(2)$}$$ Then set $$(2 - r)(2-s)(2 - t) = f(2)\tag{1}$$
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