How do you divide #(x^3+8x^2-3x+16)div(x^2+5)# using long division?

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Answer 1 · 2018-01-12T10:27:43

The quotient is #=(x+8)# and the remainder is #=-(8x+24)#

Perform the long division

#color(white)(aaaa)##x^3+8x^2-3x+16##color(white)(aaaa)##|##x^2+5#

#color(white)(aaaa)##x^3+0x^2+5x##color(white)(aaaaaaaa)##|##x+8#

#color(white)(aaaaa)##0+8x^2-8x+16#

#color(white)(aaaaaaa)##+8x^2+0x+40#

#color(white)(aaaaaaaaa)##+0-8x-24#

Therefore,

#(x^3+8x^2-3x+16)/(x^2+5)=(x+8)-(8x+24)/(x^2+5)#

The quotient is #=(x+8)# and the remainder is #=-(8x+24)#