Question 960471
Call the other factor {{{ x - a }}}
{{{ ( x - 1 )*( x + 1 )*( x - a ) = ( x^2 -1 )*( x - a ) }}}
{{{ x^3 - a*x^2 - x + a }}}
The given equation is:
{{{ x^3 + p*x^2 + q*x + 6 = 0 }}}
{{{ a = -p }}}
{{{ q = -1 }}}
{{{ a = 6 }}}
------------
The other factor is {{{ x -(-p) }}},
or {{{ x + p }}}
-------------
the equation is:
{{{ x^3 - 6x^2 - x + 6 = 0 }}}
check:
{{{ ( x - 1 )*( x + 1 )*( x - 6 ) }}}
{{{ ( x^2 - 1 )*( x - 6 ) }}}
{{{ x^3 - 6x^2 - x + 6 }}}
OK