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High Quality Content by WIKIPEDIA articles! In mathematics, a homogeneous polynomial is a polynomial whose monomials with nonzero coefficients all have the same total degree. For example, x5 + 2x3y2 + 9xy4 is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5. The polynomial x3 + 3x2y + z7 is not homogeneous, because the sum of exponents does not match from term to term. An algebraic form, or simply form, is another name for a homogeneous polynomial. The theory of algebraic forms is very extensive, and has numerous applications all over mathematics and theoretical physics.