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−3)*(x−2)*(x+2)

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