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

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

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Answer 1 · 2018-07-14T09:16:30

$x^{2} - 7 x + 15 - \frac{20}{x + 2}$ $x^2-7x+15-20/(x+2)$

Explanation:

$one way is to use the divisor as a factor in the numerator$ $"one way is to use the divisor as a factor in the numerator"$

$consider the rearranged numerator$ $"consider the rearranged numerator"$

$x^{3} - 5 x^{2} + x + 10$ $x^3-5x^2+x+10$

$= x^{2} (x + 2) - 2 x^{2} - 5 x^{2} + x + 10$ $=color(red)(x^2)(x+2)color(magenta)(-2x^2)-5x^2+x+10$

$= x^{2} (x + 2) - 7 x (x + 2) + 14 x + x + 10$ $=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(magenta)(+14x)+x+10$

$= x^{2} (x + 2) - 7 x (x + 2) + 15 (x + 2) - 30 + 10$ $=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)color(magenta)(-30)+10$

$= x^{2} (x + 2) - 7 x (x + 2) + 15 (x + 2) - 20$ $=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)-20$

$quotient = x^{2} - 7 x + 15, remainder = - 20$ $"quotient "=color(red)(x^2-7x+15)," remainder "=-20$

$\frac{x - 5 x^{2} + 10 + x^{3}}{x + 2} = x^{2} - 7 x + 15 - \frac{20}{x + 2}$ $(x-5x^2+10+x^3)/(x+2)=x^2-7x+15-20/(x+2)$

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

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