Here's a first shot, 110 characters in body only -- lacks some error check (it's going to fail with anything less than two arguements), but if you consider the second arg to be 0, then that makes sense.. :-) 
use strict;

my @poly1 = ( 2, 4, 6 );
my @poly2 = ( 3, 1, 0 );
my @poly4 = ( 5, 2, 1, 2 );

my @poly3 = p( \@poly1, \@poly2, \@poly4 );

print (join',',@poly3)."\n";

my @poly5 = p( \@poly4, \@poly1, \@poly2 );
print (join',',@poly5)."\n";

sub p {
  my$a=shift;my$b=shift;my(@c,$i,$j);for$i(0..$#$a){for$j(0..$#$b){$c[
+$i+$j]+=$$a[$i]*$$b[$j]}};@_?p(\@c,@_):\@c
}

[download]

Update: Cut down 5 more characters to 105, since you don't need to have $j around in the inner loop: 

sub p {
  my$a=shift;my$b=shift;my(@c,$i);for$i(0..$#$a){for(0..$#$b){$c[$i+$_
+]+=$$a[$i]*$$b[$_]}};@_?p(\@c,@_):\@c
}

[download]

Update #2 as per tilly's reply, fixed the return problem to add that extra character.

Dr. Michael K. Neylon - mneylon-pm@masemware.com || "You've left the lens cap of your mind on again, Pinky" - The Brain

In reply to Re: (Golf) Multiply polynomials by Masem
in thread (Golf) Multiply polynomials by tilly

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.