Help with excluding category?

I’m going nuts trying to figure out what I’m doing wrong here- I know there are a ton of other posts regarding similar situations, and I’ve sorted through many of them and tried almost everything I could come across to no avail.
I have a separate template for a blog page, and within that template, I want to exclude category 3- as that is driving a homepage carousel.

Here is what I have in ‘Blog_template.php’

<?php $paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
$categories=get_categories();
foreach($categories as $category)
{
$option .= $category->term_id.',';
}
$option .= '1';
query_posts('cat='.$option.'&paged='.$paged);
if (have_posts()) : ?>
<?php while (have_posts()) : the_post(); ?>
<div class="top-inner">
<h1><?php the_title();?></h1>
<ul>
<li><span><i>by <?php  the_author(); ?> on </i><?php the_time('F j S, Y') ?></span></li>
<li class="last"><?php the_category(', ') ?></li>
</ul>

I’ve unsucessfully tried:
$categories=get_categories('-3');
and also:
query_posts('cat=-3'.$option.'&paged='.$paged);

Am I missing something or would anyone have any direction for me?
Thanks so much for the time!