solve(x^3+x^2+x+1=0)

You can break it up into:

(x+1)(x2) +(x+1)   and further

(x+1)(x^2 +1) = 0

So either x+1 = 0  or x^2+1 =0

Which means   x=-1   or  i           Agree with guest  ,  I forgot   -i

Solve for x:
x^3+x^2+x+1 = 0

 

The left hand side factors into a product with two terms:
(x+1) (x^2+1) = 0

 

Split into two equations:
x+1 = 0 or x^2+1 = 0

 

Subtract 1 from both sides:
x = -1 or x^2+1 = 0

 

Subtract 1 from both sides:
x = -1 or x^2 = -1

 

Take the square root of both sides:
Answer: |  x = -1      or    x = i     or      x = -i                                      

 

 

\(x \Rightarrow \begin{bmatrix} x=-1 \\ x=\pm i \end{bmatrix}\)

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