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

Problem

x3+3*x2−x−3

Solution

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

(x3+3*x2)+(−x−3)

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

x2*(x+3)−1*(x+3)

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

(x2−1)*(x+3)

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+3)

Final Answer

x3+3*x2−x−3=(x−1)*(x+1)*(x+3)

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