This　paper　proposes　the　matrix　representation　of　formal　polynomials　over　max-plus　algebra　and　obtains　the　maximum　and　minimum　canonical　forms　of　a　polynomial　function　by　standardizing　this　representation　into　a　canonical　form.　A　necessary　and　sufficient　condition　for　two　formal　polynomials　corresponding　to　the　same　polynomial　function　is　derived.　Such　a　matrix　method　is　constructive　and　intuitive,　and　leads　to　a　polynomial　algorithm　for　factorization　of　polynomial　functions.　Some　illustrative　examples　are　presented　to　demonstrate　the　results.