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

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

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Answer 1 · 2018-07-15T14:16:42

The remainder is $42$ $42$ and the quotient is $= x^{3} - 3 x^{2} + 9 x - 22$ $=x^3-3x^2+9x-22$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $- 2$ $-2$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $- 1$ $-1$ $a a a a a a$ $color(white)(aaaaaa)$ $3$ $3$ $a a a a a a$ $color(white)(aaaaaa)$ $- 4$ $-4$ $a a a a$ $color(white)(aaaa)$ $- 2$ $-2$

$a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a$ $color(white)(aaaaa)$ $- 2$ $-2$ $a a a a a a$ $color(white)(aaaaaa)$ $6$ $6$ $a a a a a$ $color(white)(aaaaa)$ $- 18$ $-18$ $a a a a$ $color(white)(aaaa)$ $44$ $44$

$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ _________________________________________________________##

$a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $- 3$ $-3$ $a a a a a a$ $color(white)(aaaaaa)$ $9$ $9$ $a a a a a$ $color(white)(aaaaa)$ $- 22$ $-22$ $a a a a$ $color(white)(aaaa)$ $42$ $color(red)(42)$

The remainder is $42$ $42$ and the quotient is $= x^{3} - 3 x^{2} + 9 x - 22$ $=x^3-3x^2+9x-22$

$\frac{x^{4} - x^{3} + 3 x^{2} - 4 x - 2}{x + 2} = x^{3} - 3 x^{2} + 9 x - 22 + \frac{42}{x + 2}$ $(x^4-x^3+3x^2-4x-2)/(x+2)=x^3-3x^2+9x-22+42/(x+2)$

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

1 Answer

Explanation:

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1 Answer

Explanation:

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