Factor x^3+4x^2-9x-36

Problem

x3+4*x2−9*x−36

Solution

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

(x3+4*x2)+(−9*x−36)

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

x2*(x+4)−9*(x+4)

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

(x2−9)*(x+4)

4. Identify the difference of squares in the first factor, noting that 9=3

(x2−3)*(x+4)

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

(x−3)*(x+3)*(x+4)

Final Answer

x3+4*x2−9*x−36=(x−3)*(x+3)*(x+4)

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