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

Problem

x3−4*x2−9*x+36

Solution

1. Group terms with common factors to prepare for factoring by grouping.

(x3−4*x2)+(−9*x+36)

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

x2*(x−4)−9*(x−4)

3. Factor out the common binomial factor (x−4)

(x2−9)*(x−4)

4. Identify the difference of squares in the first factor, x2−9 which follows the pattern a2−b2=(a−b)*(a+b)

(x−3)*(x+3)*(x−4)

Final Answer

x3−4*x2−9*x+36=(x−3)*(x+3)*(x−4)

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