<PRE><B>Question 534928</B>
(5x^3)^3 = 125x^9.  Your first step was incorrect.&lt;P&gt;

125x^6 + 1 ---&gt;  (5x^2)^3 + 1 &lt;P&gt;

Set u=5x^2 so the equation becomes u^3+1.

The factor theorem states if f(a)=0 then x-a is a factor.&lt;P&gt;

f(-1) = 0 ---&gt;-1^3+1=0.  So u-1 is a factor.&lt;P&gt;
(u-1)(u^2-u+1).  (Substitute 5x^2 back in for u).&lt;P&gt;
(5x^2-1)(25x^4-5x^2+1).
</PRE>