Question 421955
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Two ways to do this.


Use synthetic division.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |-2\ \ -8\ \ h]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ }]
*[tex \LARGE \ \ \ \ \ -2\ \ |-2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |-2\ \ -8\ \ h]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |\underline{\ \ \ \ \ \ \ 4\ \ \ \ \ \ }]
*[tex \LARGE \ \ \ \ \ -2\ \ |-2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |-2\ \ -8\ \ h]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |\underline{\ \ \ \ \ \ \ 4\ \ \ \ \ \ }]
*[tex \LARGE \ \ \ \ \ -2\ \ |-2\ \ -4]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |-2\ \ -8\ \ h]
*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |\underline{\ \ \ \ \ \ \ 4\ \ \ 8\ \ }]
*[tex \LARGE \ \ \ \ \ -2\ \ |-2\ \ -4\ \ h\ +\ 8]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ h\ +\ 8\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ h\ =\ -8]


Alternatively, use the quadratic formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{8\ \pm\ \sqrt{(-8)^2\ -\ 4(-2)h}}{-4}\ =\ -2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8\ \pm\ \sqrt{64\ +\ 8h}\ =\ 8]


Hence


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \pm\ \sqrt{64\ +\ 8h}\ =\ 0]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 64\ +\ 8h\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ h\ =\ -8]


Same result.


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