Solve by Factoring 4x^3-x=0

Problem

4*x3−x=0

Solution

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

2. Factor out the common term x from the left side of the equation.

x*(4*x2−1)=0

3. Recognize that the expression inside the parentheses, 4*x2−1 is a difference of squares.

4. Apply the formula for the difference of squares a2−b2=(a−b)*(a+b) where a=2*x and b=1

x*(2*x−1)*(2*x+1)=0

5. Set each factor equal to zero according to the zero product property.

x=0

2*x−1=0

2*x+1=0

6. Solve each linear equation for x

x=0

x=1/2

x=−1/2

Final Answer

x=0,1/2,−1/2

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