Consider the polynomial [tex] x^3 + x^2 + x + 1 .[/tex] You can group first two terms and second two terms in following way:
[tex] x^3 + x^2 + x + 1 =(x^3 + x^2) + (x + 1).[/tex]
In first brackets terms [tex] x^3[/tex] and [tex] x^2[/tex] have common factor [tex] x^2[/tex], then
[tex] x^3 + x^2 + x + 1 =(x^3 + x^2) + (x + 1)=x^2(x+1)+(x+1)=(x+1)(x^2+1).[/tex]
Answer: [tex] (x+1)(x^2+1).[/tex]
