How do you divide #( x^3 + x^2 + 4x + 4 )/(x - 2 )#?

Question

How do you divide #( x^3 + x^2 + 4x + 4  )/(x - 2  )#?

Eva Adamson · Accepted Answer

#x^2+3x+10+24/(x-2)# #color(white)(..)# #" "x^3+x^2+4x+4# #color(red)(+x^2)(x-2)->color(white)(.)ul(x^3-2x^2)" "larr" Subtract"# #" "0color(white)(.)+3x^2+4x+4# #color(red)(+3x)(x-2)->" "color(white)(.)ul(3x^2-6x)" "larr" Subtract"# #" "0+10x+4# #color(red)(+10)(x-2)->" "ul(10x-20)" "larr" Subtract"# #" "color(red)(0+24" "larr" Remainder")# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #(x^3+x^2+4x+4) -:(x-2)" "color(red)(=" "x^2+3x+10+24/(x-2)#

Eva Abramson · Answer

undefined To divide (x^3 + x^2 + 4x + 4) by (x - 2), you can use long division or synthetic division. Here is the solution using long division:

x^2 + 3x + 10
    _______________________
x - 2 | x^3 + x^2 + 4x + 4
         - (x^3 - 2x^2)
         _______________
                  3x^2 + 4x
                  - (3x^2 - 6x)
                  _______________
                            10x + 4
                            - (10x - 20)
                            _______________
                                      24

Therefore, the quotient is x^2 + 3x + 10 and the remainder is 24.