One of the ANCOVA assumptions, as I read it here, says that:
Independent variables orthogonal to covariates. In traditional ANCOVA, the independents area assumed to be orthogonal to the factors. If the covariate is influenced by the categorical independents, then the control adjustment ANCOVA makes on the dependent variable prior to assessing the effects of the categorical independents will be biased since some indirect effects of the independents will be removed from the dependent.
See also the third assumption here.
Could you tell me how should I verify that this assumption is met, in a given model containing three factors and one covariate?
You can refer to SPSS or R ways of doing this.
Thank you very much