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

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

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Answer 1 · 2017-04-28T08:38:58

$4 x + 5 - \frac{18 x + 25}{x^{2} + 4}$ $4x+5-(18x+25)/(x^2+4)$

Explanation:

One way is to use the divisor as a factor in the numerator.

$Add/Subtract$ $color(magenta)"Add/Subtract"$ terms that are being added/subtracted as a consequence.

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

$4 x (x^{2} + 4) - 16 x + 5 (x^{2} + 4) - 20 - 2 x - 5$ $color(red)(4x)(x^2+4)color(magenta)(-16x)color(red)(+5)(x^2+4)color(magenta)(-20)-2x-5$

$= 4 x (x^{2} + 4) + 5 (x^{2} + 4) - 18 x - 25$ $=color(red)(4x)(x^2+4)color(red)(+5)(x^2+4)-18x-25$

$quotient = 4 x + 5, remainder = - (18 x + 25)$ $"quotient " =color(red)(4x+5), "remainder " =-(18x+25)$

$\Rightarrow \frac{4 x^{3} + 5 x^{2} - 2 x - 5}{x^{2} + 4} = 4 x + 5 - \frac{18 x + 25}{x^{2} + 4}$ $rArr(4x^3+5x^2-2x-5)/(x^2+4)=4x+5-(18x+25)/(x^2+4)$

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

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Explanation:

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

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