P princasss New member Joined Nov 12, 2010 Messages 1 Nov 12, 2010 #1 show me how to factor -4x^2y-4x^3+24xy^2

D Denis Senior Member Joined Feb 17, 2004 Messages 1,723 Nov 12, 2010 #2 princasss said: show me how to factor -4x^2y-4x^3+24xy^2 Click to expand... -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...

princasss said: show me how to factor -4x^2y-4x^3+24xy^2 Click to expand... -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...

M masters Full Member Joined Mar 30, 2007 Messages 378 Nov 12, 2010 #3 princasss said: show me how to factor \(\displaystyle -4x^2y-4x^3+24xy^2\) Click to expand... 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: \(\displaystyle 4x(-xy-x^2+6y^2)=4x(6y^2-xy-x^2)=4x(3y+x)(2y-x)\)

princasss said: show me how to factor \(\displaystyle -4x^2y-4x^3+24xy^2\) Click to expand... 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: \(\displaystyle 4x(-xy-x^2+6y^2)=4x(6y^2-xy-x^2)=4x(3y+x)(2y-x)\)