How do you divide $(12x^4+12x^3-5x^2+9x+3)/(x^2-4)$ ?

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Answer 1 · 2016-12-21T15:26:12

The answer is $=12x^2+12x+43+(57x+175)/(x^2-4)$

Let's do a long division

$color(white)(aaaa)$ $12x^4$ $color(white)(aaaa)$ $12x^3$ $color(white)(aaaa)$ $-5x^2$ $color(white)(aaaa)$ $9x$ $color(white)(aaaa)$ $3$ $∣$ $x^2-4$

$color(white)(aaaa)$ $12x^4$ $color(white)(aaaaaaaa)$ #color(white)(aaaa)-48x^2# $color(white)(aaaa)$ #color(white)(aaaaaa)# $∣$ $12x^2+12x+43$

$color(white)(aaaaaa)$ $0$ $color(white)(aaaaa)$ $12x^3$ $color(white)(aaa)$ #color(white)(aaaaaaaaaa)9x# $color(white)(aaaaaa)$

$color(white)(aaaaaa)$ #color(white)(aaaaaa)12x^3# $color(white)(aaaa)$ $+43x^2$ $color(white)(aa)$ $-48x$ $color(white)(aa)$ $+3$

$color(white)(aaaaaa)$ #color(white)(aaaaaa)0# $color(white)(aaaaaaa)$ $+43x^2$ $color(white)(aa)$ $+57x-172$ $color(white)(aaaaaa)$

$color(white)(aaaaaa)$ #color(white)(aaaaaa)# $color(white)(aaaaaaaaaaaa)$ $0$ $color(white)(aa)$ $+57x+175$ $color(white)(aaaaaa)$

Therefore,

$(12x^4+12x^3-5x^2+9x+3)/(x^2-4)$

$=12x^2+12x+43+(57x+175)/(x^2-4)$

How do you divide (12x^4+12x^3-5x^2+9x+3)/(x^2-4) (12x^4+12x^3-5x^2+9x+3)/(x^2-4) ?