Solve by Factoring 16x^3-x=0

Problem

16*x^3−x=0

Solution

1. Factor out the greatest common factor, which is x

x*(16*x^2−1)=0

2. Identify the difference of squares inside the parentheses, noting that 16*x^2=(4*x)^2 and 1=1^2

x*((4*x)^2−1^2)=0

3. Apply the difference of squares formula, a^2−b^2=(a−b)*(a+b) to factor the quadratic term.

x*(4*x−1)*(4*x+1)=0

4. Apply the Zero Product Property by setting each individual factor equal to zero.

x=0

4*x−1=0

4*x+1=0

5. Solve each linear equation for x

x=0

x=1/4

x=−1/4

Final Answer

x={0,1/4,−1/4}

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