Answer
$x=-2, \frac{1}{2}, \pm i$
$f(x)=(x-i)(x+i)(2x-1)(x+2)$
Work Step by Step
Step 1. Given
$f(x)=2x^4+3x^3+3x-2=2(x^4-1)+3x(x^2+1)=2(x^2+1)(x^2-1)+3x(x^2+1)=(x^2+1)(2x^2+3x-2)=(x^2+1)(2x-1)(x+2)$
Step 2. We can identify the zeros as:
$x=-2, \frac{1}{2}, \pm i$
Step 3. We can write the polynomial as a product of linear factors
$f(x)=(x-i)(x+i)(2x-1)(x+2)$
