Summary: A three-dimensional polynomial algebra of order \(m\) is defined by the commutation relations \([P_0,P_{\pm}] = \pm P_{\pm},\;[P_+,P_-] = \phi^{(m)}(P_0)\) where \(\phi^{(m)} (P_0)\) is an \(m\)th order polynomial in \(P_0\) with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders \(l\) and \(m\) can be combined to give two distinct \((l+m+1)\)th order polynomial algebras. This procedure follows from a generalization of the well-known Jordan–Schwinger method of construction of \(\text{su}(2)\) and \(\text{su}(1,1)\) algebras from two mutually commuting boson algebras.