Question

Can somebody help me to factorice this?

Answer 1

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)