Question

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

Answer 1

`(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)`