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

1 Answer
Jul 30, 2015

Answer:

#color(red)((4x^3+7x^2-13x-3)/(x+3) = 4x^2-5x+2-9/(x+3))#

Explanation:

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

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

Step 2. Put the divisor at the left.

#color(red)(-3)|4" "color(white)(1)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.

#-3|4" "color(white)(1)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.

#-3|4" "color(white)(1)7color(white)(1)-13" " "-3#
#" "color(white)(1)|color(white)(1)color(red)(-12)#
#" "color(white)(1)stackrel("——————————————)#
#" "color(white)(1)|4#

Step 5. Add down the column.

#-3|4" "color(white)(1)7color(white)(1)-13" " "-3#
#" "color(white)(1)|-12#
#" "color(white)(1)stackrel("——————————————)#
#" "color(white)(1)|4color(white)(1)color(red)(-5)#

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

#-3|4" "color(white)(1)7color(white)(1)-13" " "-3#
#" "color(white)(1)|-12" "color(white)(1)15" "color(white)(1)-6#
#" "stackrel("——————————————)#
#color(blue)(" "color(white)(1)|4-5" "" "2)" "color(white)(1)color(red)(-9)#

#(4x^3+7x^2-13x-3)/(x+3) = 4x^2-5x+2-9/(x+3)#

Check:

#(x+3)(4x^2-5x+2-9/(x+3)) = (x+3)(4x^2-5x+2)-9#

#= 4x^3-5x^2+2x+12x^2-15x+6-9 = 4x^3+7x^2-13x-3#