The quotient obtained when $p q^{2} + 5 p q + 6 p$ divided by $p q + 2 p$ is:

q + 3

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q - 3

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q + 2

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pq + 3p

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Solution

The correct option is A
q + 3

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

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