my @words = split /\s+/,$keyword;
my @list;
my $where = join(' OR ',
    map { 
        my $col = $_; 
        map { push @list, "%$_%"; "$col like ?" } @words
    } qw(mfg productID desc)
);
my $sth = $dbh->prepare('SELECT * FROM productTable WHERE ' . $where);
$sth->execute(@list);
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Note the use of placeholders - the ? signs. Don't use a CGI param directly in a SQL query! *) Run your CGIs with the -T switch and untaint your data (see perlsec).

*) what happens if the keyword is something like 'foo; drop productTable; select 1 where 0' ?

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}