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)#