misstamie said:
Hey everyone...I don't know why, but when factoring polynomials, I can't go further than one step. It confuses me!!!
I have been working on this problem for 4 hours! Please help!!
24a^3b+76a^2b-28ab
If you know how to do this please explain!! Thanks.
You must really be frustrated. When you have a polynomial to factor, the first thing to do is to find a common monomial factor if it exists.
To do this, look at your numerical coefficients {24, 76, 28}. Nevermind the signs at this point. Factor them into the product of prime factors. You can do this using a factor tree or inverted division, or whatever method you've been taught (I have to assume you have been taught some method).
\(\displaystyle 24=2^3\cdot3\)
\(\displaystyle 76=2^2\cdot19\)
\(\displaystyle 28=2^2\cdot7\)
To find the
GCF, find the common factor with the smallest exponent. That'd be \(\displaystyle 2^2=\boxed{4}\)
To find the common variables do the same thing, except they are already in exponential form. So, find the common variables in all three terms and use their smallest exponent. The variables are \(\displaystyle {a^3b, a^2b, ab}\). GCF would be \(\displaystyle \boxed{ab}\) .
So together the
GCF=4ab. Now factor that out of each term as
royhass suggested:
\(\displaystyle 4ab(6a^2+19a-7)\)
Now, all you have left is to see if the quadratic trinomial in parentheses can be factored. It can. See if you can continue. If not, come on back. We're chomping at the bit to be of service.
Might I suggest this site for finding GCF:
http://www.algebrahelp.com/lessons/factoring/findgcf/
And this one for factoring quadratics (choose the
hard case section}:
http://www.purplemath.com/modules/factquad.htm