Question 555661
You can complete the square:
{{{ x^2 + x - 2 = 0 }}}
{{{ x^2 + x = 2 }}}
Take 1/2 of the coefficient of {{{x}}},
square it, and add it to both sides
{{{ x^2 + x + ( 1/2 )^2 = 2 + ( 1/2 )^2 }}}
{{{ x^2 + x + 1/4 = 2 + 1/4 }}}
{{{ ( x + 1/2)^2 = 9/4 }}}
{{{ x + 1/2 = 3/2 }}}
(1) {{{ x = 1 }}}
and, also
{{{ x + 1/2 = -3/2 }}}
(2) {{{ x = -2 }}}
Rewrite (1) and (2) as
(1) {{{ x - 1 = 0 }}}
(2) {{{ x + 2 = 0 }}}
The factors are:
{{{ ( x - 1 ) * ( x + 2 ) = x^2 + x - 2 }}}