Factor x^3+3x^2-25x-75

Problem

x3+3*x2−25*x−75

Solution

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

(x3+3*x2)+(−25*x−75)

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

x2*(x+3)−25*(x+3)

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

(x2−25)*(x+3)

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

(x2−5)*(x+3)

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

(x−5)*(x+5)*(x+3)

Final Answer

x3+3*x2−25*x−75=(x+3)*(x−5)*(x+5)

Want more problems? Check here!