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

1 Answer
Nov 27, 2015

Answer:

#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)#