How do you divide $\frac{x^{2} + 20 x + 5}{x - 4}$ $(x^2+20x+5) / (x-4)$ ?

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How do you divide $\frac{x^{2} + 20 x + 5}{x - 4}$ $(x^2+20x+5) / (x-4)$ ?

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Answer 1 · 2018-03-14T06:02:14

Quotient $x + 24$ $color(green)(x + 24)$ , Remainder $\frac{101}{x - 4}$ $color(red)(101/(x-4))$

Explanation:

Let’s use synthetic division to find the quotient and remainder.

$a a a a a a a a a a a 0 a a a a a 1 a a a a 24$ $color(white)(aaa aaa aa aaa) 0 color(white)(aaa aa ) 1 color(white)(aaa a ) 24$
$color(white)(aaa aaa aa ) ———————-$
$color(white)(aaa ) 4 color(white)(aaa ) | color(white)(aaa ) 1 color(white)(aaaa) 20 color(white)(a aaa) 5$
$color(white)(aaa aaaa ) | color(white)(aa ) darr color(white)(aaa a ) 4 color(white)(aaaa) 96$
$color(white)(aaa aaa a) | color(white)(aaa ) ——- ——-$
$color(white)(aaa aaa aaa aaa ) 1 color(white)(aa aa ) 24 color(white)(aaa) 101$

Quotient $color(green)(x + 24)$ , Remainder $color(red)(101/(x-4))$

Verification : $(x + 24) * (x - 4) = x^2 + 20x -94 + 101 = x^2 + 20x + 5$

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How do you divide $\frac{x^{2} + 20 x + 5}{x - 4}$ $(x^2+20x+5) / (x-4)$ ?

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How do you divide (x^2+20x+5) / (x-4)x2+20x+5x−4(x^2+20x+5) / (x-4)?

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How do you divide $\frac{x^{2} + 20 x + 5}{x - 4}$ $(x^2+20x+5) / (x-4)$ ?