Some new canonical forms for polynomials

We give some new canonical representations for forms over $\text{cc}$. For example, a general binary quartic form can be written as the square of a quadratic form plus the fourth power of a linear form. A general cubic form in $(x_1,\mathrm{.}\mathrm{.}\mathrm{.},x_n)$ can be written uniquely as a sum of the cubes of linear forms ${\mathrm{\ell }}_{ij}(x_i,\mathrm{.}\mathrm{.}\mathrm{.},x_j)$, $1\le i\le j\le n$. A general ternary quartic form is the sum of the square of a quadratic form and three fourth powers of linear forms. The methods are classical and elementary.