Problem
ALG-B1-M02-P009 A Fourth Degree as a Quadratic Trinomial
#9
★★☆☆☆ Level 2 of 5
Factor \(x^4+x^2+1\).
Add and subtract \(x^2\).
\(x^4+x^2+1=x^4+2x^2+1-x^2=(x^2+1)^2-x^2\).
Thus the factorisation is \((x^2-x+1)(x^2+x+1)\).
A good example of artificially creating a difference of squares.