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. Simplify the expression by writing the repeated factors as a square.

(x−2)*(x+2)2

Final Answer

x3+2*x2−4*x−8=(x−2)*(x+2)2

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