Factor x^3+x^2-4x-4

Problem

x3+x2−4*x−4

Solution

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

(x3+x2)+(−4*x−4)

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

x2*(x+1)−4*(x+1)

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

(x+1)*(x2−4)

4. Identify the difference of squares in the second factor, noting that 4=2

(x+1)*(x2−2)

5. Apply the difference of squares formula a2−b2=(a−b)*(a+b) to factor x2−4

(x+1)*(x−2)*(x+2)

Final Answer

x3+x2−4*x−4=(x+1)*(x−2)*(x+2)

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