How do you divide #(5m^3 - 7m^2 + 14) / (m^2 - 2)#?

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Answer 1 · 2017-05-04T12:29:56

The quotient is #=5m-7# and the remainder is #=10m#

We perform a long division

#color(white)(aaaa)##5m^3-7m^2##color(white)(aaaaaa)##+14##|##m^2-2#

#color(white)(aaaa)##5m^3##color(white)(aaaa)##-10m##color(white)(aaaaaa)####|##5m-7#

#color(white)(aaaa)##0-7m^2##color(white)(aaaaaaaaa)##+14#

#color(white)(aaaaaa)##-7m^2##color(white)(aaaaaaaaa)##+14#

#color(white)(aaaaaaaa)##-0+10m##color(white)(aaaa)##+0#

Therefore,

#(5m^3-7m^2+14)=(m^2-2)(5m-7)+10m#