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March 2nd, 2014, 06:56 AM   #1
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How to use the factor theorem for a cubic polynomial

How exactly is the factor theorem used for a cubic polynomial 2x^3 + x^2 + x - 1, where the leading coefficient is not 1.
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March 2nd, 2014, 08:15 AM   #2
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Re: How to use the factor theorem for a cubic polynomial

I am assuming you want the complete factorization. Here is one way to do it,



Using the Rational Root Theorem and trial and error, we see is the only rational root. Next, do long division or synthetic division to get the quotient polynomial.



So far, you have this



You can stop now if you don't need the complete factoring, otherwise continue.

Using the quadratic formula to get the other two roots, you should get,





Putting it all together gives,



I leave to you the pleasure of multiplying out the RHS and confirming it is equal to the LHS.

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