Factor completely.

-5x^2 y + 10xy - 15xy^2

Question

Factor completely.

-5x^2 y + 10xy - 15xy^2

imstuck · Answer

I teach my Algebra students to deal with one thing at a time.  Let's start with the numbers.  Obviously, the idea of factoring is to take out the greatest common factor, but it has to be a factor in EVERY term, not just some of them.  So if you take out something, it has to be able to be pulled from every term.

imstuck · Answer

We see that the -5 goes into itself, obviously, but it also goes into 10 and it also goes into 15...evenly.  So we will pull out a -5 and this is what we are left with.  I'm doing it step by step.

imstuck · Answer

$$-5(x ^{2}y-2xy+3xy ^{2})$$
Notice the sign changes inside the parenthesis now that we have pulled out a negative.

imstuck · Answer

Now let's move to the x's.  We have 2 of them in the first term, only one in the second term and again only one in the third term.  So we can only factor out 1 from each term.

imstuck · Answer

$$-5x(xy-2y+3y ^{2})$$
Getting closer now.  Let's do the y's now.

imstuck · Answer

We have one in the first and second terms, and 2 in the third term, but we can only pull one from each:
$$-5xy(x-2+3y)$$

imstuck · Answer

And now it is factored completely!

skullpatrol · Answer

Good job :-)

skullpatrol · Answer

The first guideline for factoring completely is 

to factor out the greatest monomial factor first.