How do you divide #( x^5 - x^3 + 5x^2 - 10x - 75)/(x - 2 )#?

Question

How do you divide #( x^5 - x^3 + 5x^2 - 10x - 75)/(x - 2  )#?

Abigail Allen · Accepted Answer

The remainder is #color(red)(-51)# and the quotient is #=x^4+2x^3+3x^2+11x+12#

How about we execute a synthetic division?

#color(white)(aaaa)##2##color(white)(aaaaaa)##|##color(white)(aa)##1##color(white)(aaaaaa)##0##color(white)(aaaa)##-1##color(white)(aaaa)##5##color(white)(aaa)##-10##color(white)(aaa)##-75# #color(white)(aaaaaaaaaaaa)#____________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaa)##2##color(white)(aaaaa)##4##color(white)(aaaaa)##6##color(white)(aaaa)##22##color(white)(aaaaa)##24# #color(white)(aaaaaaaaaaaa)#______________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaa)##1##color(white)(aaaaa)##2##color(white)(aaaaa)##3##color(white)(aaaaa)##11##color(white)(aaa)##12##color(white)(aaaa)##color(red)(-41)#

The remainder is #color(red)(-51)# and the quotient is #=x^4+2x^3+3x^2+11x+12#

Consequently,

#(x^5-x^3+5x^2-10x-75)/(x-2)#

#=x^4+2x^3+3x^2+11x+12-11/(x-2)#

Hazel Anglin · Answer

undefined To divide (x^5 - x^3 + 5x^2 - 10x - 75) by (x - 2), you can use long division. The quotient is x^4 + 2x^3 + 4x^2 + 8x + 6, with a remainder of -63.