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 the method of common factors.

p$q^2$+5pq+6p = p$\times$q$\times$q+5$\times$p$\times$q+6$\times$p

= p($q^2$+5q+6)

Now factorize $q^2$+5q+6 by using identities.

In $q^2$+5q+6, 6 = 2$\times$3 and 2+3 = 5

or $q^2$+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)

Therefore if we divide p(q+2)(q+3) by pq+2p we get (q+3) as quotient.