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