How do you long divide #(x^[4] + 3x^[3] + 28x + 15)/( x + 5)#?

1 Answer
Jan 24, 2017

The answer is #=(x^3-2x^2+10x-22)+125/(x+5)#

Explanation:

Let's do the long division

#color(white)(aaaa)##x^4+3x^3##color(white)(aaaaaaaa)##28x+15##color(white)(aaaa)##|##x+5#

#color(white)(aaaa)##x^4+5x^3##color(white)(aaaa)####color(white)(aaaaaaaaaaaaaaaa)##|##x^3-2x^2+10x-22#

#color(white)(aaaaa)##0-2x^3#

#color(white)(aaaaaaa)##-2x^3-10x^2#

#color(white)(aaaaaaaaa)##-0+10x^2+28x#

#color(white)(aaaaaaaaaaaaa)##+10x^2+50x#

#color(white)(aaaaaaaaaaaaaaaa)##+0-22x+15#

#color(white)(aaaaaaaaaaaaaaaaaaaa)##-22x-110#

#color(white)(aaaaaaaaaaaaaaaaaaaaaa)##+0+125#

Therefore,

#(x^4+3x^3+28x+15)/(x+5)=(x^3-2x^2+10x-22)+125/(x+5)#