Degree of precision of a quadrature rule ($d$)

The degree of precision of a quadrature rule is the largest integer $d$ such that $Q(p)=I_{\rho }(p)$ for every polynomial $p$ of polynomial degree at most $d$. By linearity, checking the monomials $1,x,\dots ,x^d$ suffices. Exactness for one higher-degree polynomial alone does not raise this degree: every lower polynomial degree must also be covered.