Question

The quotient obtained 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 $2+3=5$
So, $q^2+5q+6$
$=q^2+2q+3q+6$
$=q(q+2)+3(q+2)$
$=(q+2)(q+3)$
So, $p(q^2+5pq+6p)=p(q+2)(q+3)$
Now, $\frac{p(q+2)(q+3)}{p(q+2)}=q+3$