# factoring trinomials

#### princasss

##### New member
show me how to factor
-4x^2y-4x^3+24xy^2

#### Denis

##### Senior Member
princasss said:
show me how to factor
-4x^2y-4x^3+24xy^2
-4x^2y - 4x^3 + 24xy^2
= 4x^3 + 4x^2y - 24xy^2
= 4x(x^2 + xy - 6y^2)

This is not finished; need to know if you followed what I did so far...

#### masters

##### Full Member
princasss said:
show me how to factor

$$\displaystyle -4x^2y-4x^3+24xy^2$$
Hi princasss,

You haven't told us what it is that confuses you about factoring

$$\displaystyle -4x^2y-4x^3+24xy^2$$

Can you pick out the common factors over the three terms in your expression?

Here's a little lesson that might help: http://www.algebrahelp.com/lessons/factoring/gcf/

How about $$\displaystyle -4x$$ ? Think that would work? Let's see what the other factor would be if we divided.

$$\displaystyle \frac{-4x^2y-4x^3+24xy^2}{-4x}=\frac{-4x^2y}{-4x}-\frac{4x^3}{-4x}+\frac{24xy^2}{-4x}=xy+x^2-6y^2$$

No common factors in our quotient now.

So this is what we have: $$\displaystyle -4x^2y-4x^3+24xy^2=-4x(xy+x^2-6y^2)$$

You can rearrange the terms in parentheses if you like. Or you can make the first factor positive by changing the sign of each term in the parentheses.

$$\displaystyle -4x^2y-4x^3+24xy^2=4x(-xy-x^2+6y^2)$$

And do this: $$\displaystyle 4x(-xy-x^2+6y^2)=4x(6y^2-xy-x^2)=4x(3y+x)(2y-x)$$