Factor x^3+5x^2-4x-20

Problem

x^3+5*x^2−4*x−20

Solution

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

(x^3+5*x^2)+(−4*x−20)

2. Factor out the greatest common factor from the first pair, which is x^2

x^2*(x+5)+(−4*x−20)

3. Factor out the greatest common factor from the second pair, which is −4

x^2*(x+5)−4*(x+5)

4. Factor out the common binomial (x+5) from the expression.

(x^2−4)*(x+5)

5. Identify the difference of squares in the first factor, x^2−4 which follows the pattern a^2−b^2=(a−b)*(a+b)

(x−2)*(x+2)*(x+5)

Final Answer

x^3+5*x^2−4*x−20=(x−2)*(x+2)*(x+5)

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