Question

The quotient when p$q^2$+ 5pq+6p is divided by pq+2p is

• A. q+3
• B. q-3
• C. q+2
• D. pq+3p

Answer 1

The correct option is A

q+3

First factorize the given expression by using method of common factors.
p$q^2$+5pq+6p = p×q×q+5×p×q+6×p
=p($q^2$+5q+6)
Now factorize $q^2$+5q+6 by using identities.
In $q^2$+5q+6, 6=2×3 and 2+3=5
So $q^2$+5q+6=$q^2$+2q+3q+6=q(q+2)+3(q+2)=(q+2)(q+3)
So p$q^2$+5pq+6p=p(q+2)(q+3)