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

Problem

x3+2*x2−x−2

Solution

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

(x3+2*x2)+(−x−2)

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

x2*(x+2)−1*(x+2)

3. Factor out the common binomial (x+2) from the expression.

(x2−1)*(x+2)

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

(x−1)*(x+1)*(x+2)

Final Answer

x3+2*x2−x−2=(x−1)*(x+1)*(x+2)

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