How do you divide #(2x^3-7x^2-17x-3)div(2x+3)# using long division?

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Answer 1 · 2017-01-12T08:11:05

The remainder is #=0# and the quotient is #=x^2-5x-1#

Let's go for a long division

#color(white)(aaaa)##2x^3-7x^2-17x-3##color(white)(aaaa)##∣##color(blue)(2x+3)#

#color(white)(aaaa)##2x^3+3x^2##color(white)(aaaaaaaaaaaaa)##∣##color(red)(x^2-5x-1)#

#color(white)(aaaaa)##0-10x^2-17x#

#color(white)(aaaaaaa)##-10x^2-15x#

#color(white)(aaaaaaaaaaa)##0-2x-3#

#color(white)(aaaaaaaaaaaaa)##-2x-3#

#color(white)(aaaaaaaaaaaaaa)##-0-0#

The remainder is #=0# and the quotient is #=x^2-5x-1#

#(2x^3-7x^2-17x-3)/(2x+3)=x^2-5x-1#