How do you use synthetic division to divide #(3x^3 - 17x^2 + 15x - 25) -: (x-5)#?

1 Answer
Barney V.
Jan 12, 2017

#3x^2-2x+5#

Explanation:

#color(white)(aaaa)##3x^3-17x^2=15x-25##color(white)(aaaa)##∣##color(green)(x-5)#

#color(white)(aaaa)##2x^3-15x^2##color(white)(aaaaaaaaaaaaaa ##∣##color(red)(3x^2-2x+5)#
#color(white)(aaaaa)##-----#

#color(white)(aaaaaaa)##0-2x^2+15x#

#color(white)(aaaaaaaaa)##+2x^2+10x#
#color(white)(aaaaaaaaa)##-----#

#color(white)(aaaaaaaaaaaaa)##0-5x-25#

#color(white)(aaaaaaaaaaaaaaa)##-5x-25#
#color(white)(aaaaaaaaaaaaaaa)##-----#

#color(white)(aaaaaaaaaaaaaaaa)##-0-0#

The remainder is #=0# and the quotient is #=3x^2-2x+5#

#(3x^3-17x^2+15x-25)/(x-5)=3x^2-2x+5#

#color(white)(aaaa)##3x^3-17x^2+15x-25##color(white)(aaaa)##∣##color(green)(x-5)#
#color(white)(aaaa)##x-5##color(white)(aaaaaaaaaaaaaaaaaa)##∣##color(red)(3x^2-2x+5)#
#color(white)(aaaaaaaa)##-----#

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