How do you long divide #(5x^3+x^2-x+3) / (x+1)#?

1 Answer
Nov 5, 2016

The answer is #=5x^2-4x+3#

Explanation:

Let's do the long division
#color(white)(aaaa)##5x^3+x^2-x+3##color(white)(aaa)##∣##x+1#
#color(white)(aaaa)##5x^3+5x^2##color(white)(aaaaaaaaa)##∣##5x^2-4x+3#
#color(white)(aaaaaa)##0-4x^2-x#
#color(white)(aaaaaaaa)##-4x^2-4x#
#color(white)(aaaaaaaaaaaa)##0+3x+3#
#color(white)(aaaaaaaaaaaaaaaa)##3x+3#
#color(white)(aaaaaaaaaaaaaaaaa)##0+0#

So #(5x^3+x^2-x+3)# is divisible by # (x+1) #
You can test this by doing
let #f(x)=5x^3+x^2-x+3#
the #f(-1)=-5+1+1+3=0#
This is the remainder theorem