Question 312245
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Use synthetic division:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\ |\ \ 1\ \ 1\ -10\ -6]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1]


3 times 1 is 3, and 3 plus 1 is 4


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\ |\ \ 1\ \ 1\ \ -10\ -6]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\ \ 4]


3 times 4 is 12, and 12 plus -10 is 2


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\ |\ \ 1\ \ 1\ \ -10\ -6]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\ \ \ \,12]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\ \ 4\ \ \ \ 2]


3 times 2 is 6, and 6 plus -6 is zero


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3\ |\ \ 1\ \ 1\ \ -10\ -6]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\ \ \ \,12\ \ \ 6]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\ \ 4\ \ \ \ \ 2\ \ \ 0]


Therefore the quotient is


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^3 + x^2 - 10x - 6}{x - 3}\ =\ x^2\ +\ 4x\ +\ 2]


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