How do you divide $\frac{2 x^{3} - 5 x^{2} + 4 x + 12}{x - 7}$ $(2x^3-5x^2+4x+12)/(x-7)$ ?

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How do you divide $\frac{2 x^{3} - 5 x^{2} + 4 x + 12}{x - 7}$ $(2x^3-5x^2+4x+12)/(x-7)$ ?

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Answer 1 · 2017-06-16T13:49:47

$2 x^{2} + 9 x + 67 + \frac{481}{x - 7}$ $2x^2+9x+67+481/(x-7)$

Explanation:

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

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

$2 x^{2} (x - 7) + 14 x^{2} - 5 x^{2} + 4 x + 12$ $color(red)(2x^2)(x-7)color(magenta)(+14x^2)-5x^2+4x+12$

$= 2 x^{2} (x - 7) + 9 x (x - 7) + 63 x + 4 x + 12$ $=color(red)(2x^2)(x-7)color(red)(+9x)(x-7)color(magenta)(+63x)+4x+12$

$= 2 x^{2} (x - 7) + 9 x (x - 7) + 67 (x - 7) + 469 + 12$ $=color(red)(2x^2)(x-7)color(red)(+9x)(x-7)color(red)(+67)(x-7)color(magenta)(+469)+12$

$= 2 x^{2} (x - 7) + 9 x (x - 7) + 67 (x - 7) + 481$ $=color(red)(2x^2)(x-7)color(red)(+9x)(x-7)color(red)(+67)(x-7)+481$

$quotient = 2 x^{2} + 9 x + 67, remainder = 481$ $"quotient "=color(red)(2x^2+9x+67)", remainder "=481$

$\Rightarrow \frac{2 x^{3} - 5 x^{2} + 4 x + 12}{x - 7}$ $rArr(2x^3-5x^2+4x+12)/(x-7)$

$= 2 x^{2} + 9 x + 67 + \frac{481}{x - 7}$ $=2x^2+9x+67+481/(x-7)$

Answer 2 · 2017-06-16T16:47:48

$2 x^{2} + 9 x + 67$ $color(blue)(2x^2+9x+67$ plus remainder of $481$ $color(blue)481$

Explanation:

$color(white)(.............)ul(color(blue)(2x^2+9x+67)$
$color(white)(aa)x-7$ $|$ $2x^3-5x^2+4x+12$
$color(white)(..............)ul(2x^3-14x^3)$
$color(white)(........................)9x^2+4x$
$color(white)(........................)ul(9x^2-63x)$
$color(white)(..............................)67x+12$
$color(white)(..............................)ul(67x-469)$
$color(white)(........................................)481$

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How do you divide $\frac{2 x^{3} - 5 x^{2} + 4 x + 12}{x - 7}$ $(2x^3-5x^2+4x+12)/(x-7)$ ?

2 Answers

Explanation:

Explanation:

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How do you divide (2x^3-5x^2+4x+12)/(x-7) 2x3−5x2+4x+12x−7(2x^3-5x^2+4x+12)/(x-7) ?

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Explanation:

Explanation:

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How do you divide $\frac{2 x^{3} - 5 x^{2} + 4 x + 12}{x - 7}$ $(2x^3-5x^2+4x+12)/(x-7)$ ?