Solve by Factoring x^3+3x^2-4x-12=0

Problem

x3+3*x2−4*x−12=0

Solution

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

(x3+3*x2)+(−4*x−12)=0

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

x2*(x+3)−4*(x+3)=0

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

(x2−4)*(x+3)=0

4. Factor the difference of squares (x2−4) into (x−2)*(x+2)

(x−2)*(x+2)*(x+3)=0

5. Apply the zero product property by setting each individual factor equal to zero.

x−2=0⇒x=2

x+2=0⇒x=−2

x+3=0⇒x=−3

Final Answer

x=2,−2,−3

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