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Question

snowcrystal · Answer

Factor completely 

9v^4 + 12v^3 - 18v^2 - 24v

snowcrystal · Answer

@e.mccormick

e.mccormick · Answer

Well, what number and variable can you factor out from all of those to start?

snowcrystal · Answer

i don't know how to

snowcrystal · Answer

factor with variables

e.mccormick · Answer

Well, can you see a number that would factor out of all the coefficients?

snowcrystal · Answer

3?

e.mccormick · Answer

Yes.
9v^4 + 12v^3 - 18v^2 - 24v 
becomes
3(9/3v^4 + 12/3v^3 - 18/3v^2 - 24/3v)
becomes
3(3v^4 + 4v^3 - 6v^2 - 8v )

Now, what would happen if you did the same thing with v?  Just one v.

snowcrystal · Answer

ya 1V

e.mccormick · Answer

What I mean is, if you put a v out front with the 3, then divide every term inside the ( ) by v, what does it become?

snowcrystal · Answer

Ummm im not sure

e.mccormick · Answer

Well, les see:
$3(3v^4 + 4v^3 - 6v^2 - 8v )$

$3v\left(\dfrac{3v^4}{v} + \dfrac{4v^3}{v} - \dfrac{6v^2}{v} - \dfrac{8v}{v} \right)$

Remember your rules for simplifying variables in fractions?

snowcrystal · Answer

nope

e.mccormick · Answer

$\dfrac{x^m}{x^n}=x^{m-n}$

$\dfrac{x^3}{x}=\dfrac{x^3}{x^1}=x^{3-1}=x^{2}$

e.mccormick · Answer

So, because it is over just a power of one, each exponent goes down by one.

e.mccormick · Answer

After you do that, this one will need to be factored by grouping. Here are some examples of that: http://www.regentsprep.org/Regents/math/algtrig/ATV1/revFactorGrouping.htm http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut27_gcf.htm

snowcrystal · Answer

thanks

e.mccormick · Answer

You might also want to look up factor by grouping on youtube.  The Khan Academy and PatrickJMT videos should be good.  It is easier to show than to try and explain with text.