Let ρ(x) be an mth degree polynomial which is nonnegative in [-1, 1]. Then ρ(x) can be represented in the form {[A(x)]^2 + (1 - x^2)[B(x)]^2 | for m even (1 + x)[C(x)]^2 + (1 - x)[D(x)]^2 | for m odd, auto right match where A(x), B(x), C(x), and D(x) are real polynomials whose degrees do not exceed m.