Factor x^3+3x^2-4x-12

Problem

x3+3*x2−4*x−12

Solution

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

(x3+3*x2)+(−4*x−12)

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

x2*(x+3)−4*(x+3)

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

(x2−4)*(x+3)

4. Identify the difference of squares in the first factor, noting that x2−4 can be written as x2−2

(x−2)*(x+2)*(x+3)

Final Answer

x3+3*x2−4*x−12=(x−2)*(x+2)*(x+3)

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