The given function is:

$f(x) = 2x^5 + x^4 - 18x^3 - 17x^2 + 20x + 12$

You are told that $x - 3$ is a factor of $f(x)$, and the problem asks for $f(3)$.

To find $f(3)$, you can directly substitute $x = 3$ into the function:

$f(3) = 2(3)^5 + (3)^4 - 18(3)^3 - 17(3)^2 + 20(3) + 12$

Now, let's compute this value:

$f(3) = 2(243) + 81 - 18(27) - 17(9) + 20(3) + 12$ $= 486 + 81 - 486 - 153 + 60 + 12$ $= 486 + 81 - 486 - 153 + 60 + 12 = 0$

So, $f(3) = 0$.

This makes sense since $x - 3$ is a factor of $f(x)$, and the factor theorem states that if $x - c$ is a factor of $f(x)$, then $f(c) = 0$.

Would you like more details on the steps?