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

Problem

x3−x2−4*x+4

Solution

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

(x3−x2)+(−4*x+4)

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

x2*(x−1)−4*(x−1)

3. Factor out the common binomial (x−1) from the expression.

(x2−4)*(x−1)

4. Identify the difference of squares in the first factor, noting that x2−4 is x2−2

(x−2)*(x+2)*(x−1)

Final Answer

x3−x2−4*x+4=(x−1)*(x−2)*(x+2)

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