Polynomial long division

sub poly_long_div ( @n is copy, @d ) {
    return [0], |@n if +@n < +@d;

    my @q = gather while +@n >= +@d {
        @n = @n Z- flat ( ( @d X* take ( @n[0] / @d[0] ) ), 0 xx * );
        @n.shift;
    }

    return @q, @n;
}

sub xP ( $power ) { $power>1 ?? "x^$power" !! $power==1 ?? 'x' !! '' }
sub poly_print ( @c ) { join ' + ', @c.kv.map: { $^v ~ xP( @c.end - $^k ) } }

my @polys = [ [     1, -12, 0, -42 ], [    1, -3 ] ],
            [ [     1, -12, 0, -42 ], [ 1, 1, -3 ] ],
            [ [          1, 3,   2 ], [    1,  1 ] ],
            [ [ 1, -4,   6, 5,   3 ], [ 1, 2,  1 ] ];

say '<math>\begin{array}{rr}';
for @polys -> [ @a, @b ] {
    printf Q"%s , & %s \\\\\n", poly_long_div( @a, @b ).map: { poly_print($_) };
}
say '\end{array}</math>';

Output:

1 x 2 + − 9 x + − 27 , − 123 1 x + − 13 , 16 x + − 81 1 x + 2 , 0 1 x 2 + − 6 x + 17 , − 23 x + − 14 {\displaystyle {\begin{array}{rr}1x^{2}+-9x+-27,&-123\1x+-13,&16x+-81\1x+2,&0\1x^{2}+-6x+17,&-23x+-14\\end{array}}}