How do you divide $\frac{x^{3} - 12 x^{2} - 5 x + 6}{x - 2}$ $(x^3 - 12x^2 -5x + 6)/(x-2)$ ?

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How do you divide $\frac{x^{3} - 12 x^{2} - 5 x + 6}{x - 2}$ $(x^3 - 12x^2 -5x + 6)/(x-2)$ ?

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Answer 1 · 2017-05-16T17:47:23

$x^{2} - 10 x - 25 - \frac{44}{x - 2}$ $x^2-10x-25-44/(x-2)$

Explanation:

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

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

$x^{2} (x - 2) + 2 x^{2} - 12 x^{2} - 5 x + 6$ $color(red)(x^2)(x-2)color(magenta)(+2x^2)-12x^2-5x+6$

$= x^{2} (x - 2) - 10 x (x - 2) - 20 x - 5 x + 6$ $=color(red)(x^2)(x-2)color(red)(-10x)(x-2)color(magenta)(-20x)-5x+6$

$= x^{2} (x - 2) - 10 x (x - 2) - 25 (x - 2) - 50 + 6$ $=color(red)(x^2)(x-2)color(red)(-10x)(x-2)color(red)(-25)(x-2)color(magenta)(-50)+6$

$= x^{2} (x - 2) - 10 x (x - 2) - 25 (x - 2) - 44$ $=color(red)(x^2)(x-2)color(red)(-10x)(x-2)color(red)(-25)(x-2)-44$

$\Rightarrow quotient = x^{2} - 10 x - 25, remainder = - 44$ $rArr"quotient "=color(red)(x^2-10x-25)," remainder "=-44$

$\Rightarrow \frac{x^{3} - 12 x^{2} - 5 x + 6}{x - 2} = x^{2} - 10 x - 25 - \frac{44}{x - 2}$ $rArr(x^3-12x^2-5x+6)/(x-2)=x^2-10x-25-44/(x-2)$

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How do you divide $\frac{x^{3} - 12 x^{2} - 5 x + 6}{x - 2}$ $(x^3 - 12x^2 -5x + 6)/(x-2)$ ?

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How do you divide $\frac{x^{3} - 12 x^{2} - 5 x + 6}{x - 2}$ $(x^3 - 12x^2 -5x + 6)/(x-2)$ ?