Question 756502
If {{{x+a}}} is a factor in
{{{f(x)=x^2 + px + q}}} and in
{{{g(x)=x^2 + mx + n}}}, then
{{{f(-a)=a^2 -pa+ q=0}}} and
{{{g(-a)=a^2 - ma + n=0}}}.
That would give as a system of equations that looks confusing, but we only need to solve it partially.
{{{system(a^2 -pa+ q=0,a^2 - ma + n=0)}}} --> {{{a^2 -pa+ q=a^2 - ma + n}}} --> {{{-pa+ q=- ma + n}}} --> {{{-pa+ q+ma=n}}} --> {{{-pa+ma=n-q}}} --> {{{ma-pa=n-q}}} --> {{{ (m-p)a=n-q}}} --> {{{highlight(a=(n-q)/(m-p))}}}