My Math Forum How to factor 3*(x^4) + 4*(x^3) - 3

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 June 14th, 2012, 11:04 AM #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 x-intercepts but I'm not sure how to factor polynomials with degrees greater than 2..
 June 14th, 2012, 11:13 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 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 root-finding technique, such as the Newton-Raphson method, to approximate the roots to the desired accuracy. Using the latter option, we find: $x\approx1.58464,\,0.779333$
 June 14th, 2012, 11:21 AM #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, 05:38 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 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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