Finding the zeros and intercepts---help / check answer?

Hi, again I am rusty at math (I haven't done it in two years). There are no solutions in my book for my homework, so could someone double check that I have the right idea?

1) Find the zeros of the given function f.

$\displaystyle f(x)=x^3-x^2-2x$

$\displaystyle f(x)=x(x^2-x-2)$

$\displaystyle f(x)=x(x-2)(x+1) $

So, are the zeros x=2, x=-1, and x=0?

One more...

2) Find the x- and y-intercepts, if any, of the graph of the given function f. Do not graph.

$\displaystyle f(x)=(2x-3)(x^2+8x+16)$

$\displaystyle f(x)=2x^3+16x^2+32x-3x^2-24x+13$

$\displaystyle f(x)=2x^3+13x^2+8x+13$

$\displaystyle f(x)=x(2x^2+13x+21)$

$\displaystyle f(x)=x(2x+7)(x+3)$

For the X-intercepts I got...

(-7/2,0), (-3,0), (0,0)

How do I find the y-intercepts then? Do I plug in zero for "x"? If I do, wouldn't the y-intercept be just (0,0)?

Thank you so much in advanced!