Matrix factorization of a polynomial

A matrix factorization of a polynomial is an technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial "p" without linear terms can be written as a "AB" = "pI", where "A" and "B" are square matrices and "I" is the identity matrix. Given the polynomial "p", the matrices "A" and "B" can be found by elementary methods.
The polynomial "x"2 + "y"2 is irreducible over R["x","y"], but can be written as
formula_1