How do you use synthetic division to divide #4x^3 + 7x^2 – 13x – 3# by #x-7#?

1 Answer
Jul 31, 2015

Answer:

#(4x^3+7x^2-13x-3)/(x-7) = color(blue)(4x^2+35x+232)+color(red)(1621)/(x-7)#

Explanation:

Step 1. Write only the coefficients of #x# in the dividend inside an upside-down division symbol.

#|4" "" "7color(white)(1)-13" "" "-3#
#|color(white)(1)#
#stackrel("—————————————————)#

Step 2. Put the divisor at the left.

#color(red)(7)|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|color(white)(1)#
#" "stackrel("—————————————————)#

Step 3. Drop the first coefficient of the dividend below the division symbol.

#7|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|color(white)(1)#
#" "stackrel("—————————————————)#
#color(white)(1)|color(red)(4)#

Step 4. Multiply the result by the constant, and put the product in the next column.

#7|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|" "" "color(red)(28)#
#" "stackrel("—————————————————)#
#color(white)(1)|4#

Step 5. Add down the column.

#7|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|" "" "28#
#" "stackrel("—————————————————)#
#color(white)(1)|4" "color(white)(1)color(red)(35)#

Step 6. Repeat Steps 4 and 5 until you can go no farther.

#7|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|" "" "28" "color(white)(1)245" "color(white)(1)1624#
#" "stackrel("—————————————————)#
#color(blue)(color(white)(1)|4" "color(white)(1)35" "color(white)(1)232)" "color(white)(1)color(red)(1621)#

#(4x^3+7x^2-13x-3)/(x-7) = 4x^2+35x+232+1621/(x-7)#

Check:

#(x-7)(4x^2+35x+232+1621/(x-7)) = (x-7)(4x^2+35x+232)-1621 = 4x^3+35x^2+232x-28x^2-245x-1624+1621#

#= 4x^3+7x^2-13x-3#