How do you divide #(6x^4 + 2x^3 – 6x^2 – 14x – 1 )/( 3x + 1) #?

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Answer 1 · 2017-03-02T08:10:05

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

We perform a polynomial long 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)(aaaaaaaaaaaa)##-6x^2-2x#

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

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

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

The remainder is #=3#

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