Factor x^3+5x^2-x-5

Problem

x3+5*x2−x−5

Solution

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

(x3+5*x2)+(−x−5)

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

x2*(x+5)−1*(x+5)

3. Factor out the common binomial (x+5) from the expression.

(x2−1)*(x+5)

4. Identify the difference of squares in the first factor, as x2−1 can be written as x2−1

(x−1)*(x+1)*(x+5)

Final Answer

x3+5*x2−x−5=(x−1)*(x+1)*(x+5)

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