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June 14th, 2012, 12:04 PM  #1 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  How to factor 3*(x^4) + 4*(x^3)  3
I know it has two xintercepts but I'm not sure how to factor polynomials with degrees greater than 2..

June 14th, 2012, 12:13 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs  Re: How to factor 3*(x^4) + 4*(x^3)  3
The rational root theorem shows us the real roots are not rational. You have two options: a) Use the formula for the roots of the general quartic (very messy). b) Use a numeric rootfinding technique, such as the NewtonRaphson method, to approximate the roots to the desired accuracy. Using the latter option, we find: 
June 14th, 2012, 12:21 PM  #3 
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  Re: How to factor 3*(x^4) + 4*(x^3)  3
How come we can't find irrational roots like we can find them with the quadratic formula for degree 2 polynomials?

June 14th, 2012, 06:38 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs  Re: How to factor 3*(x^4) + 4*(x^3)  3
We can, but as I mentioned, it's quite messy. Here is an article outlining some methods.


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3x4, 4x3, factor 
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