Question 331340
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Use the Rational Roots Theorem to determine that the possible rational roots of the equation *[tex \Large x^3\ -\ 4x^2\ +\ x\ -\ 4\ =\ 0] are:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \pm1,\,\pm2,\,\pm4]


Use Synthetic Division to exclude


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \pm1,\,\pm2,\,-4]


And to show that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 4]


is a factor of the given polynomial.  If you need a refresher on Synthetic Division, see:  <a href="http://www.purplemath.com/modules/synthdiv.htm">Purple Math Synthetic Division</a>


The quotient from the synthetic division was


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 1]


Which, as we know, factors to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ i\ \ ] and *[tex \LARGE x\ -\ i]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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