Answer:
(r^2 - r - 1)(r^2 + r - 1).
Step-by-step explanation:
r^4 - 3r^2 + 1
We need to make this into a perfect square so the r^4 and the 1 fit the bill but not the -3r^2 so we have to correct for that.
A perfect square would be:
r^4 - 2r^2 + 1 ( = (r^2 - 1)^2 )
But we need -3r^2 so we add - r^2 at the end:
= (r^4 - 2r^2 + 1) - r^2 So now we have the difference of 2 squares and we write:
(r^2 - 1)^2 - r^2
= (r^2 - 1 - r)(r^2 - 1 + r)
= (r^2 - r - 1)(r^2 + r - 1)
