How do you find the quotient of #(9n^3-13n+8)div(3n-1)# using long division?

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Answer 1 · 2017-04-11T17:02:09

The quotient is #=3n^2+n-4#

Let's perform the long division

#color(white)(aaaa)##9n^3##color(white)(aaaaaa)##-13n+8##|##3n-1#

#color(white)(aaaa)##9n^3-3n^2##color(white)(aaaaaaaaa)####|##3n^2+n-4#

#color(white)(aaaaaa)##0+3n^2-13n#

#color(white)(aaaaaaaa)##+3n^2-n#

#color(white)(aaaaaaaaa)##+0-12n+8#

#color(white)(aaaaaaaaaaaaa)##-12n+4#

#color(white)(aaaaaaaaaaaaaaa)##-0+4#

So,

#(9n^3-13n+8)/(3n-1)=(3n^2+n-4)+4/(3n-1)#