Answer
$(q+1)(q+5p)$.
Work Step by Step
The given polynomial is
$=q^2+q+5pq+5p$
Group the terms.
$=(q^2+q)+(5pq+5p)$
Factor each group.
$=q(q+1)+5p(q+1)$
Factor out $(q+1)$.
$=(q+1)(q+5p)$
Hence, the complete factor of the polynomial is $(q+1)(q+5p)$.
