Factor x^3+2x^2-9x-18

Problem

x3+2*x2−9*x−18

Solution

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

(x3+2*x2)+(−9*x−18)

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

x2*(x+2)−9*(x+2)

3. Factor out the common binomial (x+2) from the expression.

(x+2)*(x2−9)

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

(x+2)*(x2−3)

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

(x+2)*(x−3)*(x+3)

Final Answer

x3+2*x2−9*x−18=(x+2)*(x−3)*(x+3)

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