Question

How do you long divide `(x^3-7x-6) div (x+1)`?

Answer 1

The nominator can be factored as

#x^3-7x-6=x^3-6x-x-6= x^3-x-6(x+1)= x(x-1)(x+1)-6(x+1)= (x+1)*[x(x-1)+6]#

Hence

#(x^3-7x-6)/(x+1)=(x+1)*[x(x-1)+6]/(x+1)= x*(x-1)+6=x^2-x+6#