How do you divide #(x^3-8x^2-6) / (x-2)#?

Question

Eli Assouline · Accepted Answer

The quotient is #=x^2-6x-12# and the remainder is #-30#

Perform a long division

#color(white)(aaaa)##x^3-8x^2+0x-6##color(white)(aaaa)##|##x-2#

#color(white)(aaaa)##x^3-2x^2##color(white)(aaaaaaaaaaaa)##|##x^2-6x-12#

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

#color(white)(aaaaaa)##-6x^2+12x#

#color(white)(aaaaaaaaa)##0-12x-6#

#color(white)(aaaaaaaaaaa)##-12x+24#

#color(white)(aaaaaaaaaaaaaaa)##0-30#

The quotient is #=x^2-6x-12# and the remainder is #-30#

#(x^3-8x^2-6)/(x-2)=x^2-6x-12-30/(x-2)#

Eva Abramson · Answer

undefined To divide (x^3-8x^2-6) by (x-2), you can use long division or synthetic division. Here is the solution using long division:

x^2 - 6x + 4
    ___________________
x - 2 | x^3 - 8x^2 - 6
         - (x^3 - 2x^2)
         _______________
                  -6x^2 - 6
                  + (6x^2 - 12x)
                  _______________
                            -12x - 6
                            + (12x - 24)
                            _______________
                                      -30

Therefore, the quotient is x^2 - 6x + 4 and the remainder is -30.