Question

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

Answer 1

`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 `3pq`

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

So our final answer is `3pq(p2 - 3q + 12)`