How do you divide #(5x^4-3x^3+2x^2-1)div(x^2+4)# using long division?

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Answer 1 · 2017-02-03T08:01:49

The answer is #=(5x^2-3x-18)+(12x+71)/(x^2+4)#

Let's do the long division

#color(white)(aaaa)##5x^4-3x^3+2x^2-1##color(white)(aaaaaaaa)##|##x^2+4#

#color(white)(aaaa)##5x^4##color(white)(aa aaaa)##+20x^2##color(white)(aaaaaaaaaaa)##|##5x^2-3x-18#

#color(white)(aaaa)##0-3x^3##color(white)(aa a)##-18x^2##color(white)(aaaaaaa)#

#color(white)(aaaaaa)##-3x^3##color(white)(aaaa)##-18x^2-12x-1##color(white)(aaaaaaa)#

#color(white)(aaaaaaaa)##0##color(white)(aaaaa)##-18x^2-12x##color(white)(a)##-72#

#color(white)(aaaaaaaaaaaaaaaaa)##0##color(white)(aaa)##+12x##color(white)(aa)##+71#

Therefore,

#(5x^4-3x^3+2x^2-1)/(x^2+4)=5x^2-3x-18+(12x+71)/(x^2+4)#

The quotient is #=5x^2-3x-18#

The remainder is #=12x+71#