A polynomial p(x) is nonnegative (p(x) ≥ 0 for all x) if it can be written as a sum of squares (SOS): p(x) = Σ qᵢ(x)². Hilbert's 17th Problem (1900) asked whether every nonneg polynomial is a sum of squares of rationals — answered affirmatively by Artin (1927). The SOS condition is equivalent to the existence of a positive semidefinite matrix Q such that p(x) = z(x)ᵀ Q z(x), where z(x) is a vector of monomials. This converts polynomial optimization to an SDP. The decomposition shown here displays each squared component with its color-coded contribution to the total polynomial.