在数学中，齐次多项式是指各项的总次数均相同的多项式 ，例如 就是一个五次的双变元齐次多项式，其各项的总次数都是五。

齐次多项式有时也称作代数形式或形式。二次齐次多项式是二次型，在特征不等于二的域（如实数或复数域）上可以用对称矩阵表示。代数形式的理论很广，并在数学及物理中有大量应用。

In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree. For example, is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5. The polynomial is not homogeneous, because the sum of exponents does not match from term to term. A polynomial is homogeneous if and only if it defines a homogeneous function. An algebraic form, or simply form, is a function defined by a homogeneous polynomial. A binary form is a form in two variables. A form is also a function defined on a vector space, which may be expressed as a homogeneous function of the coordinates over any basis.