How do you divide $\frac{4 x^{4} - 5 x^{2} - 2 x + 24}{(x + 4)}$ $(4x^4 -5x^2-2x+24)/((x + 4) )$ ?

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How do you divide $\frac{4 x^{4} - 5 x^{2} - 2 x + 24}{(x + 4)}$ $(4x^4 -5x^2-2x+24)/((x + 4) )$ ?

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Answer 1 · 2017-10-06T08:10:24

$4 x^{3} - 16 x^{2} + 59 x - 238 + \frac{976}{x + 4}$ $4x^3-16x^2+59x-238+976/(x+4)$

Explanation:

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

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

$4 x^{3} (x + 4) - 16 x^{3} - 5 x^{2} - 2 x + 24$ $color(red)(4x^3)(x+4)color(magenta)(-16x^3)-5x^2-2x+24$

$= 4 x^{3} (x + 4) - 16 x^{2} (x + 4) + 64 x^{2} - 5 x^{2} - 2 x + 24$ $=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(magenta)(+64x^2)-5x^2-2x+24$

$= 4 x^{3} (x + 4) - 16 x^{2} (x + 4) + 59 x (x + 4) - 236 x - 2 x + 24$ $=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(magenta)(-236x)-2x+24$

$= 4 x^{3} (x + 4) - 16 x^{2} (x + 4) + 59 x (x + 4)$ $=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(red)$
$= - 238 (x + 4) + 952 + 24$ $color(white)(=)color(red)(-238)(x+4)color(magenta)(+952)+24$

$quotient = 4 x^{3} - 16 x^{2} + 59 x - 238$ $"quotient "=color(red)(4x^3-16x^2+59x-238)$

$remainder = 976$ $"remainder "=976$

$\Rightarrow \frac{4 x^{4} - 5 x^{2} - 2 x + 24}{x + 4}$ $rArr(4x^4-5x^2-2x+24)/(x+4)$

$= 4 x^{3} - 16 x^{2} + 59 x - 238 + \frac{976}{x + 4}$ $=4x^3-16x^2+59x-238+976/(x+4)$

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How do you divide $\frac{4 x^{4} - 5 x^{2} - 2 x + 24}{(x + 4)}$ $(4x^4 -5x^2-2x+24)/((x + 4) )$ ?

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Explanation:

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How do you divide $\frac{4 x^{4} - 5 x^{2} - 2 x + 24}{(x + 4)}$ $(4x^4 -5x^2-2x+24)/((x + 4) )$ ?