You can use factor theorem to factorize this equation : x^3+2x^2+2x+1
What are the factors of 1 ?
1 AND -1
-1 is satisfying the equation to 0
x+1 is factor of x^3+2x^2+2x+1
Now use division method .
Quotient will be
(1 + x + x^2)
So x^3+2x^2+2x+1 = (x+1)(1 + x + x^2)