How do you use synthetic division to divide #(5x^3+18x^2+7x-6)div(x+3)#?

2 Answers

Answer:

#5x^2+3x-2#

Explanation:

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Oct 5, 2017

Answer:

Quotient is #5x^2+3x-2# andremainder is #0#. See the process below.

Explanation:

To divide #f(2)# for #5x^3+18x^2+7x-6# by #x+3#

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

#color(white)(1)|color(white)(X)5" "color(white)(X)18color(white)(XX)+7" "" "-6#
#color(white)(1)|" "color(white)(X)#
#" "stackrel("—————————————)#

Two Put #-3# in the divisor at the left as #x+3=0# gives #x=-3#

#-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6#
#color(white)(xx)|" "color(white)(X)#
#" "stackrel("—————————————)#

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

#-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6#
#color(white)(xx)|" "color(white)(X)#
#" "stackrel("—————————————)#
#" "color(white)(1)|color(white)(X)color(red)#

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

#-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6#
#color(white)(xx)|" "color(white)(X)#
#" "stackrel("—————————————)#
#" "color(white)(1)|color(white)(X)color(blue)5#

Five Add down the column.

#-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6#
#" "color(white)(1)|" "color(white)(X)-15#
#color(white)(1)stackrel("—————————————)#
#color(white)(xx)|color(white)(X)color(blue)5color(white)(XXX)color(red)3#

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

#-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6#
#" "color(white)(1)|" "color(white)(X)-15color(white)(X)-9color(white)(XXX)6#
#color(white)(1)stackrel("—————————————)#
#color(white)(xx)|color(white)(X)color(blue)5color(white)(XXX)color(red)3color(white)(X)color(red)-2color(white)(XXX)color(red)0#

Hence remainder is #0# and quotient is #5x^2+3x-2#