How do you factor $x^3 - 2x + 1$ ?

Question

30205 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-19T08:13:44

It is

$x^3-2x+1=x^3-x-x+1=x(x^2-1)-(x-1)=x(x-1)(x+1)-(x-1)=(x-1)*(x^2+x-1)$

Now for the trinomial $x^2+x-1$ the roots are

$x_(1,2)=[-1^2(+-)sqrt(1^2+4)]/2=>x_1=(-1+sqrt5)/2 and x_2=(1+sqrt5)/2$

So finally the factorization is

$x^3-2x+1=-1/4 (x-1)*(-2 x+sqrt(5)-1)*(2 x+sqrt(5)+1)$

How do you factor x^3 - 2x + 1x^3 - 2x + 1?