A more efficient way to construct a coefficient array?

This is a follow-up to an older question: Using coeffs to extract a matrix. The answer there is great, but I'm just wondering if there is a more efficient way of performing this operation:

I have a polynomial function of many symbolic variables, and I want to extract the 'coefficient matrix' from this polynomial. Every term in the polynomial has only two factors of these symbolic variables, i.e.

The coefficient matrix I want to extract is the one that would produce precisely this polynomial if I evaluated the vector-matrix-vector product:

where here x is a vector whose entries are all these symbolic variables, and K is the coeffient matrix.

I have found that using hessian() to do this has been very slow as the polynomial expression becomes large. Is this the best method available in MATLAB?