How do you divide using synthetic division: #(2u^4 - 5u^3 - 12u^2 + 2u - 8)/(u - 4)#?

2 Answers
Oct 19, 2017

Answer:

#(2u^4-5u^3-12u^2+2u-8)/(u-4)=color(red)(2u^3+3u^2+2)#
with a Remainder of #color(blue)0#
#color(white)("XXX")#(see below for solution method using synthetic division)

Explanation:

#{: ([0],,,color(grey)(u^4),color(grey)(u^3),color(grey)(u^2),color(grey)(u^1),color(grey)(u^0)), ([1],," | ",2,-5,-12,+2,-8), ([2],ul(+color(white)("xxx"))," | ",ul(color(white)(0)),ul(+8),ul(+12),ul(+0),ul(+8)), ([3],xxcolor(magenta)4," | ",color(red)2,color(red)(+3),color(white)(+0)color(red)(0),color(white)("+")color(red)(2),color(white)("+")0), ([4],,,color(grey)(u^3),color(grey)(u^2),color(white)(+0)color(grey)(u^1),color(white)("+")color(grey)(u^0)color(white)("+"),color(blue)("R")) :}#

Rows [0] and [4] are not really part of the synthetic division; they are here for reference purposes only.

Row [1] are the coefficients of the variables in row [0]

Values in Row [3] are the sum of the values in the same column from Rows [1] and [2]

Values in Row [2] are the product of the values from the previous column of Row [3] and #color(magenta)4# where #color(magenta)4# is the value of #u# necessary to make the divisor #(u-4)# equal to #0#

Oct 19, 2017

Answer:

The remainder is #color(red)(0)# and the quotient is #=2u^3+3u^2+2#

Explanation:

Let's perform the synthetic division

#color(white)(aa)##4##color(white)(aaaaa)##|##color(white)(aaa)##2##color(white)(aaaaa)##-5##color(white)(aaaaaa)##-12##color(white)(aaaaa)##2##color(white)(aaaaaa)##-8#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaa)##|##color(white)(aaaa)##color(white)(aaaaaaa)##8##color(white)(aaaaaaa)##12##color(white)(aaaaa)##0##color(white)(aaaaaaaa)##8#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaa)##|##color(white)(aaa)##2##color(white)(aaaaaaa)##3##color(white)(aaaaaaaa)##0##color(white)(aaaaa)##2##color(white)(aaaaaaaa)##color(red)(0)#

The remainder is #color(red)(0)# and the quotient is #=2u^3+3u^2+0u+2#

#(2u^4-5u^3-12u^2+2u-8)/(u-4)=2u^3+3u^2+0u+2#