How do you use long division to divide #(x^3+4x^2-3x-12)div(x-3)#?

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Answer 1 · 2017-04-12T12:54:54

The quotient is #=(x^2+7x+18)# and the remainder is #=42#

Let's perform the long division

#color(white)(aaaa)##x^3+4x^2-3x-12##color(white)(aaaa)##|##x-3#

#color(white)(aaaa)##x^3-3x^2##color(white)(aaaaaaaaaaaaa)##|##x^2+7x+18#

#color(white)(aaaaa)##0+7x^2-3x#

#color(white)(aaaaaaa)##+7x^2-21x#

#color(white)(aaaaaaaaaa)##0+18x-12#

#color(white)(aaaaaaaaaaaa)##+18x-54#

#color(white)(aaaaaaaaaaaaaa)##+0+42#

Therefore,

#(x^3+4x^2-3x-12)/(x-3)=x^2+7x+18+42/(x-3)#

The quotient is #=(x^2+7x+18)# and the remainder is #=42#