How do you divide #(5x^4+14x^3+9x)div(x^2+3x)# using long division?

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Answer 1 · 2016-11-14T15:16:20

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

Let's do the long division

#color(white)(aaaa)##5x^4+14x^3+9x##color(white)(aaaa)##∣##x^2+3x#

#color(white)(aaaa)##5x^4+15x^3##color(white)(aaaaaaaaa)##∣##5x^2-x+3#

#color(white)(aaaaaa)##0-x^3#

#color(white)(aaaaaaaa)##-x^3-3x^2#

#color(white)(aaaaaaaaaa)##0+3x^2+9x#

#color(white)(aaaaaaaaaaaa)##+3x^2+9x#

#color(white)(aaaaaaaaaaaaaaaa)##0+0#

#(5x^4+14x^3+9x)/(x^2+3x)=5x^2-x+3#

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