Factoring Polynomials: 24a^3b + 76a^2b - 28ab

misstamie

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Jul 20, 2008
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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. :)
 
Re: Factoring Polynomials

Show your work. Start by factoring out the factor \(\displaystyle 4ab\). Then use the rules in your textbook about factoring quadratic expressions. This should only take a few minutes, not four hours.
 
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
 
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