How do you divide $(2 x^{4} + 7) \div (x^{2} - 1)$ $(2x^4+7)div(x^2-1)$ using long division?

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Answer 1 · 2016-12-15T17:18:41

The remainder is $= 9$ $=9$ and the quotient is $= 2 x^{2} + 2$ $=2x^2+2$

Let's do the long division

$a a a a$ $color(white)(aaaa)$ $2 x^{4}$ $2x^4$ $a a a a$ $color(white)(aaaa)$ $a a a a$ $color(white)(aaaa)$ $+ 7$ $+7$ $∣$ $∣$ $x^{2} - 1$ $x^2-1$

$a a a a$ $color(white)(aaaa)$ $2 x^{4} - 2 x^{2}$ $2x^4-2x^2$ $a a a a$ $color(white)(aaaa)$ $a$ $color(white)(a)$ #∣2x^2+2#

$a a a a a$ $color(white)(aaaaa)$ $0 + 2 x^{2} + 7$ $0+2x^2+7$ $a a a a$ $color(white)(aaaa)$

$a a a a a a a$ $color(white)(aaaaaaa)$ $+ 2 x^{2} - 2$ $+2x^2-2$ $a a a a$ $color(white)(aaaa)$

$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $+ 0 + 9$ $+0+9$ $a a a a$ $color(white)(aaaa)$

The remainder is $= 9$ $=9$ and the quotient is $= 2 x^{2} + 2$ $=2x^2+2$

$\frac{2 x^{4} + 7}{x^{2} - 1} = 2 x^{2} + 2 + \frac{9}{x^{2} - 1}$ $(2x^4+7)/(x^2-1)=2x^2+2+9/(x^2-1)$

How do you divide (2x^4+7)div(x^2-1)(2x4+7)÷(x2−1)(2x^4+7)div(x^2-1) using long division?