Solve for x 4x^3-16x=0

Problem

4*x3−16*x=0

Solution

1. Identify the greatest common factor in the expression 4*x3−16*x

2. Factor out the common term 4*x from both terms on the left side.

4*x*(x2−4)=0

3. Recognize that x2−4 is a difference of squares, which follows the pattern a2−b2=(a−b)*(a+b)

4. Factor the quadratic expression further.

4*x*(x−2)*(x+2)=0

5. Apply the Zero Product Property, which states that if a product of factors is zero, at least one of the factors must be zero.

4*x=0⇒x=0

x−2=0⇒x=2

x+2=0⇒x=−2

Final Answer

x=0,2,−2

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