How do you divide #(2x^3+x+3 )/(x+1)#?

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Answer 1 · 2017-01-23T08:34:42

The answer is #=2x^2-2x+3#

You can do a long division

#color(white)(aaaa)##2x^3##color(white)(aaaaaaa)##x+3##color(white)(aaaaa)##|##x+1#

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

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

#color(white)(aaaaaaa)##-2x^2-2x#

#color(white)(aaaaaaaa)##-0+3x+3#

#color(white)(aaaaaaaaaaaa)##+3x+3#

#color(white)(aaaaaaaaaaaaa)##+0+0#

Therefore,

#(2x^3+2x^2)/(x+1)=2x^2-2x+3#