How do you divide $\frac{x^{4} + 2 x^{3} + 5 x^{2} + 6 x - 32}{x - 4}$ $(x^4+2x^3+ 5 x^2+6x-32)/(x-4)$ ?

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How do you divide $\frac{x^{4} + 2 x^{3} + 5 x^{2} + 6 x - 32}{x - 4}$ $(x^4+2x^3+ 5 x^2+6x-32)/(x-4)$ ?

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Answer 1 · 2017-06-05T09:32:03

The remainder is $= 456$ $=456$ and the quotient is $= x^{3} + 6 x^{2} + 29 x + 122$ $=x^3+6x^2+29x+122$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $4$ $4$ $a a a a a$ $color(white)(aaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a a a$ $color(white)(aaaaaa)$ $2$ $2$ $a a a a a a$ $color(white)(aaaaaa)$ $5$ $5$ $a a a a a$ $color(white)(aaaaa)$ $6$ $6$ $a a a a a a a$ $color(white)(aaaaaaa)$ $- 32$ $-32$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ _________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $4$ $4$ $a a a a a a$ $color(white)(aaaaaa)$ $24$ $24$ $a a a a$ $color(white)(aaaa)$ $116$ $116$ $a a a a a a$ $color(white)(aaaaaa)$ $488$ $488$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ ________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a a$ $color(white)(aaaaa)$ $6$ $6$ $a a a a a a$ $color(white)(aaaaaa)$ $29$ $29$ $a a a a$ $color(white)(aaaa)$ $122$ $122$ $a a a a a a$ $color(white)(aaaaaa)$ $456$ $color(red)(456)$

$\frac{x^{4} + 2 x^{3} + 5 x^{2} + 6 x - 32}{x - 4} = (x^{3} + 6 x^{2} + 29 x + 122) + \frac{456}{x - 4}$ $(x^4+2x^3+5x^2+6x-32)/(x-4)=(x^3+6x^2+29x+122)+(456)/(x-4)$

The remainder is $= 456$ $=456$ and the quotient is $= x^{3} + 6 x^{2} + 29 x + 122$ $=x^3+6x^2+29x+122$

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How do you divide $\frac{x^{4} + 2 x^{3} + 5 x^{2} + 6 x - 32}{x - 4}$ $(x^4+2x^3+ 5 x^2+6x-32)/(x-4)$ ?

1 Answer

Explanation:

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How do you divide x4+2x3+5x2+6x−32x−4(x^4+2x^3+ 5 x^2+6x-32)/(x-4) ?

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How do you divide $\frac{x^{4} + 2 x^{3} + 5 x^{2} + 6 x - 32}{x - 4}$ $(x^4+2x^3+ 5 x^2+6x-32)/(x-4)$ ?