Compute the resultant of the polynomials $f(x)=x^2y+3xy-1$ and $g(x)=6x^2+y^2-4$ Consider these two polynomials: 
$$f=x^2y+3xy-1$$
$$g=6x^2+y^2-4$$
I need to compute their resultant, denoted in my textbook as $h=Res(f,g,x)$. 
Here's where I need help: setting up the Sylvester Matrix. I could be missing something obvious, but from the definitions I've read online, I kept getting a matrix like so:
$X =\begin{bmatrix} 1 & 0 & 0 & 6 & 0 & 0\\3 & 1 & 0 & 1 & 6 & 0\\-1 & 3 & 1 & -4 & 1 & 6\\0 & -1 & 3 & 0 & -4 & 1\\0 & 0 & -1 & 0 & 0 & -4\\\end{bmatrix}$
My understanding is that $X$ should be a square matrix- what am I missing?
Thanks in advance. 
UPDATE:
Is this more like it?
$X =\begin{bmatrix} y & 0 & 6 \\-1 & y & 0 \\0 & -1 & y^2-4 \\\end{bmatrix}$

Write your polynomials as
$$
yx^2+ (3xy)-1
$$
and
$$
-6x^2+ (y^2-4)
$$
As polynomials in $x$, these have degree two, so your matrix should be a $4 \times 4$ matrix.
$$
\begin{pmatrix}
y & 3y & -1 & 0 \\
0 & y & 3y & -1 \\
-6 & 0 & y^2-4 & 0 \\
0 & -6 & 0 & y^2-4
\end{pmatrix}
$$
Taking the determinant gives 
$$
y^{6}-62 y^{4}-12 y^{3}+232 y^{2}+48 y+36
$$
This can also be computed in Macaulay2 by the commands:
i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : f1 = x^2*y+3*x*y-1

      2
o2 = x y + 3x*y - 1

o2 : R

i3 : f2 = -6*x^2+y^2-4

         2    2
o3 = - 6x  + y  - 4

o3 : R

i4 : resultant(f1,f2,x)

      6      4      3       2
o4 = y  - 62y  - 12y  + 232y  + 48y + 36

o4 : R

