how do you find the zeros for this equation 1/2x^3-x by factoring

Question

1/2x^3-x finding the zeros by factoring

Answer 1

1/2 x^3 - x

factor out an x

x (1/2 x^2 - 1)

set each equal to zero so x = 0 is one solution

1/2 x^2 - 1 = 0

add 1 to both sides

1/2 x^2 = 1

multiply both sides by 2

x^2 = 2

square root both sides keeping in mind that you need both positive and negative

x = sqroot (2) and x = -sqroot (2)

final answers x = 0, sqroot (2), -sqroot(2)