Decide the factorization of the polynomial m2+5m+mt+5t

Formula used:
The factors of a polynomial can be find by taking a common factor and this method is called factor by grouping,
$ab+ac+bd+cd=a(b+c)+d(b+c)$
$=(a+d)(b+c)$
Or,
$ab-ac+bd-cd=a(b-c)+d(b-c)$
$=(a+d)(b-c)$
Calculation:
Consider the polynomial $m^2+5m+mt+5t$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$m^2+5m+mt+5t=(m^2+Sm)+(mt+5t)$
$=m(m+5)+t(m+5)$
As, $(m+5)$ is the common factor of the polynomial factor it out as follows:
$m^2+5m+mt+5t=(m+5m)+(mt+5t)$
$=m(m+5)+t(m+5)$
$=(m+5)(m+1)$
The factorization of the polynomial $m^2+5m+mt+5t$ is $(m+5)(m+t)$.
Check the result as follows:
$(m+5)(m+t)=m\ast m+m\ast t+5\ast m+5\ast t$
$=m^2+mt+5m+5t$
$=m^2+5m+mt+5t$
Thus, the factorization of the polynomial $m^2+5m+mt+5t$ is $(m+5)(m+t)$.