How do you factor $(1+x-x^2)^2$ ?

Question

1806 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-28T18:09:11

$(1+x-x^2)^2=(x-1/2-sqrt(5/2))^2(x-1/2+sqrt(5)/2)^2$

$(1+x-x^2)^2$

$=(x^2-x-1)^2$

$=((x-1/2)^2-5/4)^2$

$=((x-1/2)^2-(sqrt(5)/2)^2)^2$

$=(x-1/2-sqrt(5/2))^2(x-1/2+sqrt(5)/2)^2$

How do you factor (1+x-x^2)^2(1+x-x^2)^2?