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

Problem

x3+x2−x−1

Solution

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

(x3+x2)+(−x−1)

2. Factor out the greatest common factor from each pair.

x2*(x+1)−1*(x+1)

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

(x2−1)*(x+1)

4. Identify the difference of squares in the first factor, x2−1 which follows the pattern a2−b2=(a−b)*(a+b)

(x−1)*(x+1)*(x+1)

5. Simplify the expression by combining the identical binomial factors into a square.

(x−1)*(x+1)2

Final Answer

x3+x2−x−1=(x−1)*(x+1)2

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