Question 305472
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Provide the missing terms:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x^3\ +\ 0x^2\ +\ 0x\ +\ 7]


*[tex \Large x] goes into *[tex \Large 4x^3\ \ \ ],*[tex \Large 4x^2] times.  Write *[tex \Large 4x^2] over the *[tex \Large 0x^2].


*[tex \Large 4x^2] times *[tex \Large -2] is *[tex \Large -8x^2].  Write *[tex \Large -8x^2] under the *[tex \Large 0x^2].  *[tex \Large 4x^2] times *[tex \Large x] is *[tex \Large 4x^3].  Write *[tex \Large 4x^3] under the *[tex \Large 4x^3].


Subtract (Change the sign and Add) *[tex \Large 4x^3\ -\ 8x^2] from *[tex \Large 4x^3\ +\ 0x^2].  Equals *[tex \Large 8x^2].


Bring down the *[tex \Large 0x] to form *[tex \Large 8x^2\ +\ 0x].


*[tex \Large x] goes into *[tex \Large 8x^2\ \ \ ],*[tex \Large 8x] times.  Write *[tex \Large 8x] over the *[tex \Large 0x].


*[tex \Large 8x] times *[tex \Large -2] is *[tex \Large -16x].  Write *[tex \Large -16x] under the *[tex \Large 0x].  *[tex \Large 8x] times *[tex \Large x]
 is *[tex \Large 8x^2].  Write *[tex \Large 8x^2] under the *[tex \Large 8x^2].


Subtract (Change the sign and add) the *[tex \Large 8x^2\ -\ 16x] from  the *[tex \Large 8x^2\ -\ 0x]. Equals *[tex \Large 16x]


Bring down the *[tex \Large 7] to form *[tex \Large 16x\ +\ 7].


*[tex \Large x] goes into *[tex \Large 16x\ \ \ ],*[tex \Large 16] times.  Write *[tex \Large 16] over the *[tex \Large 7].


*[tex \Large 16] times *[tex \Large -2] is *[tex \Large -32].  Write *[tex \Large -32] under the *[tex \Large 7].  *[tex \Large 16] times *[tex \Large x]
 is *[tex \Large 16x].  Write *[tex \Large 16x] under the *[tex \Large 16x].


Subtract (Change the sign and add) the *[tex \Large 16x\ -\ 32] from  the *[tex \Large 16x\ +\ 7]. Equals *[tex \Large 39]


Quotient is *[tex \Large 4x^2\ +\ 8x\ +\ 16]


Remainder is *[tex \Large 39]


Hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4x^3\ +\ 7}{x\ -\ 2}\ =\ 4x^2\ +\ 8x\ +\ 16\ +\ \frac{39}{x\ -\ 2}]


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