How do you use long division to divide $(6x^3+10x^2+x+8)div(2x^2+1)$ ?

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Answer 1 · 2017-05-17T15:24:34

The quotient is $=3x+1$ and the remainder is $=-2x+3$

Let's perform the long division

$color(white)(aaaa)$ $2x^2+1$ $color(white)(aaaa)$ $|$ $6x^3+10x^2+x+8$ $color(white)(aaaa)$ $|$ $3x+5$

$color(white)(aaaaaaaaaaaaaaaa)$ $6x^3$ $color(white)(aa aaaaa)$ $+3x$ $color(white)(aaaa)$

$color(white)(aaaaaaaaaaaaaaaaa)$ $0$ $color(white)(aa aa)$ $10x^2$ $-2x$ $color(white)(aaaa)$

$color(white)(aaaaaaaaaaaaaaaaa)$ $color(white)(aa aaa)$ $10x^2$ $color(white)(aaaa)$ $+5$ $color(white)(aaaa)$

$color(white)(aaaaaaaaaaaaaaaaa)$ $color(white)(aa aaaa)$ $0$ $color(white)(aaaaaa)$ $+3$ $color(white)(aaaa)$

$color(white)(aaaaaaaaaaaaaaaaa)$ $color(white)(aa aaaaaa)$ $-2x$ $color(white)(aa)$ $+3$ $color(white)(aaaa)$

$(6x^3+10x^2+x+8)/(2x^2+1)=(3x+5)+(-2x+3)/(2x^2+1)$

How do you use long division to divide (6x^3+10x^2+x+8)div(2x^2+1)(6x^3+10x^2+x+8)div(2x^2+1)?