How do you divide #6x^4+2x^3-6x^2-14x-1# by #3x+1# using long division?

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Answer 1 · 2016-11-16T11:08:31

The quotient is #=(2x^3-2x-4)#
The remainder is #=3#

Let's do the division

#color(white)(aaaa)##6x^4+2x^3-6x^2-14x-1##color(white)(aaaa)##∣##3x+1#

#color(white)(aaaa)##6x^4+2x^3##color(white)(aaaaaaaaaaaaaaaaaa)##∣##2x^3-2x-4#

#color(white)(aaaaaaa)##0+0-6x^2-14x#

#color(white)(aaaaaaaaaaaaa)##-6x^2-2x#

#color(white)(aaaaaaaaaaaaaa)##-0-12x-1#

#color(white)(aaaaaaaaaaaaaaaaaa)##-12x-4#

#color(white)(aaaaaaaaaaaaaaaaaaaa)##-0+3#

#(6x^4+2x^3-6x^2-14x-1)/(3x+1)=(2x^3-2x-4)+3/(3x+1)#

The quotient is #=2x^3-2x-4#

The remainder is #=3#