How do you use synthetic division to divide #(x^3-729)/(x-9)#?

1 Answer
Jan 23, 2017

Answer:

Quotient is #x^2+9x+81# and remainder is #0#.

Explanation:

To divide #x^3-729# or #x^3+0x^2+0x-729# by #x+2#

One Write the coefficients of #x# in the dividend inside an upside-down division symbol.

#color(white)(1)|color(white)(X)1" "color(white)(X)0color(white)(XX)0" "" "-729#
#color(white)(1)|" "color(white)(X)#
#" "stackrel("—————————————)#

Two As #x-9=0# gives #x=9# put #9# at the left.

#9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729#
#color(white)(xx)|" "color(white)(XX)#
#" "stackrel("—————————————)#

Three Drop the first coefficient of the dividend below the division symbol.

#9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729#
#color(white)(xx)|" "color(white)(X)#
#" "stackrel("—————————————)#
#color(white)(xx)|color(white)()color(red)1#

Four Multiply the result by the constant, and put the product in the next column.

#9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729#
#color(white)(xx)|" "color(white)(Xx)9#
#" "stackrel("—————————————)#
#color(white)(xx)|color(white)()color(blue)1#

Five Add down the column.

#9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729#
#color(white)(xx)|" "color(white)(Xx)9#
#" "stackrel("—————————————)#
#color(white)(xx)|color(white)()color(blue)1color(white)(xxx)color(red)9#

Six Repeat Steps Four and Five until you can go no farther.

#9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729#
#color(white)(xx)|" "color(white)(Xx)9color(white)(XX)81color(white)(XXxx)729#
#" "stackrel("—————————————)#
#color(white)(xx)|color(white)()color(blue)1color(white)(xxx)color(red)9color(white)(XX)color(red)81color(white)(XXXXX)color(red)0#

Hence, Quotient is #x^2+9x+81# and remainder is #0#.