How do you factor #x^3+x^2+x+1#?

1 Answer
Apr 24, 2018

Answer:

#(x+1)(x+i)(x-i)#

Explanation:

#color(blue)"factor by grouping"#

#=color(red)(x^2)(x+1)color(red)(+1)(x+1)#

#"take out the "color(blue)"common factor "(x+1)#

#=(x+1)(color(red)(x^2+1))#

#"we can factor "x^2+1" by solving "x^2+1=0#

#x^2+1=0rArrx^2=-1rArrx=+-i#

#rArrx^2+1=(x+i)(x-i)#

#rArrx^3+x^2+x+1=(x+1(x+i)(x-i)#