Question 1043391
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  4  |    1   -1  -20   20   64  -64
     |         4   12  -32  -48   64
     -------------------------------
          1    3   -8  -12   16    0

 -4  |    1    3   -8  -12   16
     |        -4    4   16  -16
     --------------------------
          1   -1   -4    4    0
</pre>
Hence,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^5\ -\ x^4\ -\ 20x^3\ +\ 20x^2\ +\ 64x\ -\ 64\ =\ (x\ -\ 4)(x\ +\ 4)(x^3\ -\ x^2\ -\ 4x\ +\ 4)]


Factor *[tex \LARGE (x^3\ -\ x^2\ -\ 4x\ +\ 4)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^3\ -\ 4x\ -\ x^2\ +\ 4]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x(x^2\ -\ 4)\ -\ (x^2\ -\ 4)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 1)(x\ -\ 2)(x\ +\ 2)]


So the complete factorization is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 4)(x\ +\ 4)(x\ -\ 1)(x\ -\ 2)(x\ +\ 2)]




John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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