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

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

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Answer 1 · 2017-02-15T14:12:12

$2 x^{2} + 2 x - 1 + \frac{4}{x - 2}$ $2x^2+2x-1+4/(x-2)$

Explanation:

One way is to express the numerator as factors of the divisor (x-2)

$2 x^{2} (x - 2) + (+ 4 x^{2} - 2 x^{2}) - 5 x + 6$ $color(red)(2x^2)(x-2)+(color(blue)(+4x^2)-2x^2)-5x+6$

$= 2 x^{2} (x - 2) + 2 x (x - 2) + (+ 4 x - 5 x) + 6$ $=color(red)(2x^2)(x-2)color(red)(+2x)(x-2)+(color(blue)(+4x)-5x)+6$

$= 2 x^{2} (x - 2) + 2 x (x - 2) - 1 (x - 2) + (- 2 + 6)$ $=color(red)(2x^2)(x-2)color(red)(+2x)(x-2)color(red)(-1)(x-2)+(color(blue)(-2)+6)$

$\Rightarrow \frac{2 x^{3} - 2 x^{2} - 5 x + 6}{x - 2}$ $rArr(2x^3-2x^2-5x+6)/(x-2)$

$= 2 x^{2} + 2 x - 1 + \frac{4}{x - 2}$ $=color(red)(2x^2+2x-1)+4/(x-2)$

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

1 Answer

Explanation:

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How do you divide (2x^3 - 2x^2 -5x + 6)/(x-2)2x3−2x2−5x+6x−2(2x^3 - 2x^2 -5x + 6)/(x-2)?

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Explanation:

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