Question

from x^4 + x^2 + 1, how do we get (x^2 + x + 1)(x^2 -x + 1) ?

Answer 1

complete the square

Answer 2

i get (x^2 + 1/2)^2 + 3/4

Answer 3

add and subtract \(x^2\) and rewrite as
\[x^4+x^2+1=x^4+2x^2+1-x^2\] completes the square

Answer 4

ah get it, thanks a bunch

Answer 5

now you have the difference of two squares
\[(x^2+1)^2-x^2\] rewrite as
\[(x^2+1+x)(x^2+1-x)\]

Answer 6

yw