How do you divide $\frac{x^{3} + 4 x^{2} - 17 x - 16}{x - 4}$ $( x^3+4x^2-17x-16 )/(x-4)$ ?

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How do you divide $\frac{x^{3} + 4 x^{2} - 17 x - 16}{x - 4}$ $( x^3+4x^2-17x-16 )/(x-4)$ ?

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Answer 1 · 2018-04-20T12:29:15

$x^{2} + 8 x + 15 + \frac{44}{x - 4}$ $x^2+8x+15+44/(x-4)$

Explanation:

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

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

$x^{2} (x - 4) + 4 x^{2} + 4 x^{2} - 17 x - 16$ $color(red)(x^2)(x-4)color(magenta)(+4x^2)+4x^2-17x-16$

$= x^{2} (x - 4) + 8 x (x - 4) + 32 x - 17 x - 16$ $=color(red)(x^2)(x-4)color(red)(+8x)(x-4)color(magenta)(+32x)-17x-16$

$= x^{2} (x - 4) + 8 x (x - 4) + 15 (x - 4) + 60 - 16$ $=color(red)(x^2)(x-4)color(red)(+8x)(x-4)color(red)(+15)(x-4)color(magenta)(+60)-16$

$= x^{2} (x - 4) + 8 x (x - 4) + 15 (x - 4) + 44$ $=color(red)(x^2)(x-4)color(red)(+8x)(x-4)color(red)(+15)(x-4)+44$

$quotient = x^{2} + 8 x + 15, remainder = 44$ $"quotient "=color(red)(x^2+8x+15)," remainder "=44$

$\Rightarrow \frac{x^{3} + 4 x^{2} - 17 x - 16}{x - 4}$ $rArr(x^3+4x^2-17x-16)/(x-4)$

$= x^{2} + 8 x + 15 + \frac{44}{x - 4}$ $=x^2+8x+15+44/(x-4)$

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How do you divide $\frac{x^{3} + 4 x^{2} - 17 x - 16}{x - 4}$ $( x^3+4x^2-17x-16 )/(x-4)$ ?

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How do you divide ( x^3+4x^2-17x-16 )/(x-4)x3+4x2−17x−16x−4( x^3+4x^2-17x-16 )/(x-4)?

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How do you divide $\frac{x^{3} + 4 x^{2} - 17 x - 16}{x - 4}$ $( x^3+4x^2-17x-16 )/(x-4)$ ?