The solution of linear quadratic predictive optimal control problems for systems represented in state-equation form, but using a polynomial systems approach, is considered. A multi-step cost-function is used that includes future set-point information. A novel method is introduced for computing the vector of future controls and for solving a simpler optimization problem for the current control. It is shown that the polynomial solution approach is particularly valuable, even for systems represented in state equation form, since the effect on the controller of reference, noise and disturbance models is more transparent.