Factorize the given polynomial : 15pq+15+9q+25p.

To factorize the given polynomial: 15pq + 15 + 9q + 25p, we will follow these steps:

Group terms: First, let's group the terms in pairs that might allow factoring by common factors.

15pq + 15 + 9q + 25p can be grouped as: (15pq + 25p) + (9q + 15)

Factor out common factors from each group:

From the first group (15pq + 25p), we can factor out 5p: 15pq + 25p = 5p(3q + 5)

From the second group (9q + 15), we can factor out 3: 9q + 15 = 3(3q + 5)

Factor out the common binomial factor: Now, we see that both groups contain the common factor (3q + 5). So, we can factor out (3q + 5) from the entire expression:

5p(3q + 5) + 3(3q + 5) = (3q + 5)(5p + 3)

So, the factorized form of the given polynomial is:

(3q + 5)(5p + 3)