How do you divide #(x^3 + x^2 +4x -6) / (x^2 -3x +2) # using polynomial long division?

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Answer 1 · 2016-12-23T04:02:31

The quotient is #=(x+4)# and the remainder #=14(x-1)#

Let's do the long division

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

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

#color(white)(aaaaa)##0+4x^2+2x-6#

#color(white)(aaaaaaa)##+4x^2-12x+8#

#color(white)(aaaaaaaaa)##0+14x-14#

Therefore,

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

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

The quotient is #=(x+4)# and the remainder #=14(x-1)#