We are asked to solve the equation 2x³ - 32x = 0. First off, we can see that the variable x appears in both terms on the left-hand side of the equation. Therefore, we can factor it out. We can also factor out a common factor of 2 from both terms.
2x³ - 32x = 0
2x(x² - 16) = 0
We can use the difference of squares pattern to further simplify the equation.
2x(x + 4)(x - 4) = 0
Now, using the Zero Product Property, set each term to zero.
2x = 0
x = 0
x + 4 = 0
x = -4
x - 4 = 0
x = 4
Therefore, the solutions to the equation 2x³ - 32x are 0, -4, and 4. Hope this helped and have a great day!
