Factor x^3-2x^2-4x+8

Problem

x3−2*x2−4*x+8

Solution

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

(x3−2*x2)+(−4*x+8)

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

x2*(x−2)−4*(x−2)

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

(x2−4)*(x−2)

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

(x−2)*(x+2)*(x−2)

5. Combine the identical factors to simplify the final expression.

(x−2)2*(x+2)

Final Answer

x3−2*x2−4*x+8=(x−2)2*(x+2)

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