How do you find the quotient of #(x^3+2x^2-7x-2)/(x-2)# using long division?

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Answer 1 · 2017-02-02T11:11:53

The quotient is #=color(red)(x^2+4x+1)#

Let's do the long division

#color(white)(aaaa)##x^3+2x^2-7x-2##color(white)(aaaa)##|##color(blue)(x-2)#

#color(white)(aaaa)##x^3-2x^2##color(white)(aaaaaaaaaaaa)##|##color(red)(x^2+4x+1)#

#color(white)(aaaaa)##0+4x^2-7x#

#color(white)(aaaaaaa)##+4x^2-8x#

#color(white)(aaaaaaaaa)##+0+x-2#

#color(white)(aaaaaaaaaaaaa)##+x-2#

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

The remainder is #=0# and the quotient is #color(red)(x^2+4x+1)#