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

Let's first factorise the numerator of 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.
Note that $2+3=5$ and $2\times 3=6$
So, $q^2+5q+6=(q+2)(q+3)$

$[q^2+5q+6=q^2+2q+3q+6$
$=q(q+2)+3(q+2)$
$=(q+2)(q+3)]$

So, $p(q^2+5pq+6p)=p(q+2)(q+3)$

$\therefore \frac{p{q}^2+5pq+6p}{pq+2p}=\frac{p(q+2)(q+3)}{p(q+2)}=q+3$