How do you find the quotient of #(2w^3+3w^2-5w+1)div(w+3)# using long division?

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Answer 1 · 2017-02-07T14:21:50

The quotient is #=color(red)(2w^2-3w+4)#

Let's do the long division

#color(white)(aaaa)##2w^3+3w^2-5w+1##color(white)(aaaa)##|##color(blue)(w+3)#

#color(white)(aaaa)##2w^3+6w^2##color(white)(aaaaaaaaaaaa)##|##color(red)(2w^2-3w+4)#

#color(white)(aaaaaa)##0-3w^2-5w#

#color(white)(aaaaaaaa)##-3w^2-9w#

#color(white)(aaaaaaaaaa)##-0+4w+1#

#color(white)(aaaaaaaaaaaaaa)##+4w+12#

#color(white)(aaaaaaaaaaaaaaaa)##+0-11#

Therefore

The remainder is #=-11#

The quotient is #=color(red)(2w^2-3w+4)#