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June 14th, 2012, 11:04 AM   #1
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How to factor 3*(x^4) + 4*(x^3) - 3

I know it has two x-intercepts but I'm not sure how to factor polynomials with degrees greater than 2..
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June 14th, 2012, 11:13 AM   #2
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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 root-finding technique, such as the Newton-Raphson method, to approximate the roots to the desired accuracy.

Using the latter option, we find:

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June 14th, 2012, 11:21 AM   #3
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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?
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June 14th, 2012, 05:38 PM   #4
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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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