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

Problem

x3+4*x2−x−4

Solution

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

(x3+4*x2)+(−x−4)

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

x2*(x+4)−1*(x+4)

3. Factor out the common binomial (x+4) from the expression.

(x2−1)*(x+4)

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+4)

Final Answer

x3+4*x2−x−4=(x−1)*(x+1)*(x+4)

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