Factor x^3+5x^2-25x-125

Problem

x3+5*x2−25*x−125

Solution

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

(x3+5*x2)+(−25*x−125)

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

x2*(x+5)−25*(x+5)

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

(x2−25)*(x+5)

4. Identify the difference of squares in the first factor, noting that 25=5

(x2−5)*(x+5)

5. Apply the difference of squares formula a2−b2=(a−b)*(a+b) to factor x2−25

(x−5)*(x+5)*(x+5)

6. Simplify the expression by writing the repeated factors as a square.

(x−5)*(x+5)2

Final Answer

x3+5*x2−25*x−125=(x−5)*(x+5)2

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