# How do you factor completely 3p^3q-9pq^2+36pq?

Nov 27, 2015

3p3q−9pq2+36pq = 3pq(p2 - 3q + 12)

#### Explanation:

What is present in every part of this equation? what is the lowest common factor of these?

Well we have a $p$ present in all of them, and we also have a $q$ in all of them as well.

Now is there another greatest common factor among $3$,$9$, and $36$? Yes! It is $3$.

So we can divide every term in the equation by $3 p q$

Take out $3 p q$ by dividing every term by $3 p q$:
3pq((3p3q)/(3pq)−(9pq2)/(3pq)+(36pq)/(3pq))

So our final answer is $3 p q \left(p 2 - 3 q + 12\right)$