How do you divide $\frac{x^{5} - x^{3} + 5 x^{2} - 10 x - 75}{x - 2}$ $( x^5 - x^3 + 5x^2 - 10x - 75)/(x - 2 )$ ?

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How do you divide $\frac{x^{5} - x^{3} + 5 x^{2} - 10 x - 75}{x - 2}$ $( x^5 - x^3 + 5x^2 - 10x - 75)/(x - 2 )$ ?

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Answer 1 · 2017-08-06T12:12:08

The remainder is $- 51$ $color(red)(-51)$ and the quotient is $= x^{4} + 2 x^{3} + 3 x^{2} + 11 x + 12$ $=x^4+2x^3+3x^2+11x+12$

Explanation:

Let's perform a synthetic division

$a a a a$ $color(white)(aaaa)$ $2$ $2$ $a a a a a a$ $color(white)(aaaaaa)$ $∣$ $|$ $a a$ $color(white)(aa)$ $1$ $1$ $a a a a a a$ $color(white)(aaaaaa)$ $0$ $0$ $a a a a$ $color(white)(aaaa)$ $- 1$ $-1$ $a a a a$ $color(white)(aaaa)$ $5$ $5$ $a a a$ $color(white)(aaa)$ $- 10$ $-10$ $a a a$ $color(white)(aaa)$ $- 75$ $-75$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ ________________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a$ $color(white)(aaaaa)$ $2$ $2$ $a a a a a$ $color(white)(aaaaa)$ $4$ $4$ $a a a a a$ $color(white)(aaaaa)$ $6$ $6$ $a a a a$ $color(white)(aaaa)$ $22$ $22$ $a a a a a$ $color(white)(aaaaa)$ $24$ $24$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ ______________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $1$ $1$ $a a a a a$ $color(white)(aaaaa)$ $2$ $2$ $a a a a a$ $color(white)(aaaaa)$ $3$ $3$ $a a a a a$ $color(white)(aaaaa)$ $11$ $11$ $a a a$ $color(white)(aaa)$ $12$ $12$ $a a a a$ $color(white)(aaaa)$ $- 41$ $color(red)(-41)$

The remainder is $- 51$ $color(red)(-51)$ and the quotient is $= x^{4} + 2 x^{3} + 3 x^{2} + 11 x + 12$ $=x^4+2x^3+3x^2+11x+12$

Therefore,

$\frac{x^{5} - x^{3} + 5 x^{2} - 10 x - 75}{x - 2}$ $(x^5-x^3+5x^2-10x-75)/(x-2)$

$= x^{4} + 2 x^{3} + 3 x^{2} + 11 x + 12 - \frac{11}{x - 2}$ $=x^4+2x^3+3x^2+11x+12-11/(x-2)$

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How do you divide $\frac{x^{5} - x^{3} + 5 x^{2} - 10 x - 75}{x - 2}$ $( x^5 - x^3 + 5x^2 - 10x - 75)/(x - 2 )$ ?

1 Answer

Explanation:

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Explanation:

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How do you divide $\frac{x^{5} - x^{3} + 5 x^{2} - 10 x - 75}{x - 2}$ $( x^5 - x^3 + 5x^2 - 10x - 75)/(x - 2 )$ ?