Factor x^3+x^2+x+1

Problem

x^3+x^2+x+1

Solution

1. Group the terms into two pairs to prepare for factoring by grouping.

(x^3+x^2)+(x+1)

2. Factor out the greatest common factor from the first pair of terms, which is x^2

x^2*(x+1)+1*(x+1)

3. Factor out the common binomial (x+1) from the entire expression.

(x+1)*(x^2+1)

Final Answer

x^3+x^2+x+1=(x+1)*(x^2+1)

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