How do you divide $\frac{- 3 x^{3} + 15 x^{2} - x - 2}{x + 1}$ $( -3x^3+ 15x^2-x-2)/(x + 1 )$ ?

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How do you divide $\frac{- 3 x^{3} + 15 x^{2} - x - 2}{x + 1}$ $( -3x^3+ 15x^2-x-2)/(x + 1 )$ ?

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Answer 1 · 2017-06-19T09:58:19

$- 3 x^{2} + 18 x - 19 + \frac{17}{x + 1}$ $-3x^2+18x-19+17/(x+1)$

Explanation:

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

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

$- 3 x^{2} (x + 1) + 3 x^{2} + 15 x^{2} - x - 2$ $color(red)(-3x^2)(x+1)color(magenta)(+3x^2)+15x^2-x-2$

$= - 3 x^{2} (x + 1) + 18 x (x + 1) - 18 x - x - 2$ $=color(red)(-3x^2)(x+1)color(red)(+18x)(x+1)color(magenta)(-18x)-x-2$

$= - 3 x^{2} (x + 1) + 18 x (x + 1) - 19 (x + 1) + 19 - 2$ $=color(red)(-3x^2)(x+1)color(red)(+18x)(x+1)color(red)(-19)(x+1)color(magenta)(+19)-2$

$\Rightarrow \frac{- 3 x^{3} + 15 x^{2} - x - 2}{x + 1}$ $rArr(-3x^3+15x^2-x-2)/(x+1)$

$=(cancel((x+1))(color(red)(-3x^2+18x-19)))/cancel((x+1))+17/(x+1)$

$=-3x^2+18x-19+17/(x+1)$

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How do you divide $\frac{- 3 x^{3} + 15 x^{2} - x - 2}{x + 1}$ $( -3x^3+ 15x^2-x-2)/(x + 1 )$ ?

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How do you divide ( -3x^3+ 15x^2-x-2)/(x + 1 )−3x3+15x2−x−2x+1( -3x^3+ 15x^2-x-2)/(x + 1 )?

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How do you divide $\frac{- 3 x^{3} + 15 x^{2} - x - 2}{x + 1}$ $( -3x^3+ 15x^2-x-2)/(x + 1 )$ ?