Let $P$ be a commutative Noetherian ring, $\mathfrak{𝔠}$ be an ideal of $P$ which is generated by a regular sequence of length four, $f$ be a regular element of $P$, and $\overline{P}$ be the hypersurface ring $P∕(f)$. Assume that $\mathfrak{𝔠}:f$ is a grade four Gorenstein ideal of $P$. We give a resolution $N$ of $\overline{P}∕\mathfrak{𝔠}\overline{P}$ by free $\overline{P}$-modules. The resolution $N$ is built from a differential graded algebra resolution of $P∕(\mathfrak{𝔠}:f)$ by free $P$-modules, together with one homotopy map. In particular, we give an explicit form for the matrix factorization which is the infinite tail of the resolution $N$.