Question

I need help finding the zeros

Answer 1

The zeros of the polynomial function
`\(f(x) = 2x^3 - 18x\)` are
`\(x = 0, -3, \text{ and } 3\)`, obtained by factoring and solving for x.

To determine the zeros of the polynomial function
`\(f(x) = 2x^3 - 18x\)`, we need to find the values of x for which f(x) = 0.

1. Factor Out Common Terms:

`f(x) = 2x(x^2 - 9)`

2. Set Each Factor Equal to Zero:

`2x = 0 \quad \text{or} \quad x^2 - 9 = 0`

3. Solve for x:

- From 2x = 0, we get x = 0.

- From x^2 - 9 = 0, we factor as (x + 3)(x - 3) = 0, giving x = -3 or
x = 3.

Therefore, the zeros of the polynomial function f(x) are x = 0, -3, and 3. These are the values for which f(x) = 0.