Question 191251
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If you found the depressed equation twice, you should be at an easy to solve quadratic.


Check your work based on the following results when I performed the polynomial long division:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{P(x)}{x - (-2)} = \frac{x^4+4x^3-16x-16}{x + 2} = x^2 +2x^2 -4x -8]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2 +2x^2 -4x -8}{x + 2} = x^2 - 4]


And


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 - 4 = (x + 2)(x - 2)], hence the roots are 


-2 (with a multiplicity of 3) and 2.


I used polynomial long division, but synthetic division would work just as well.  A common error when performing these division operations is failing to explictly specify all orders of the variable in the dividend.  In other words, you have to divide into:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  x^4 + 4x^3 + 0x^2 - 16x - 16]


or if you are using synthetic division, your first line of coefficients must look like:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1\  4\  0\  -16\  -16]


Another possible source of error would be if you were dividing by x - 2.  Remember, if the root is -2, then the factor is x + 2, and that should have been your divisor.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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