calculation and analysis – how can one eliminate the results for which constant values ​​are assigned to the symbols?

As an exercise (relative to my assignment) Perform a constrained integration on more than[-1,1]^ 6 – giving a "probability of separability"), I launched the command

p = integrate[Boole[a2 + b2 z > z^2 && a5 + b5 z > a2 + b2 z], {z, -1, 1}];

and got a result with LeafCount[p]= 8354.

Since, in fact, I want to consider a2, b2, a5, b5 as multivariate expressions for later integrations, I would like to eliminate these (multiple) parts of the results for $ p $ Constant values, such as those containing a2 == 0, are assigned to one of the four symbols because they would be zero-valued at subsequent integrations. (I've briefly tried using NumberQ – but that did not make it possible to reach the scheduled eliminations.)

As a note concerning the display indicated above, I mean to substitute for a2, the constant term of the expression – considered as a quadratic polynomial in $ z $– for the C2 constraint here (after its division by $ (1-t ^ 2) $) and for b2, the coefficient of $ z $; and for a5, the constant term of expression considered in the same way for quadratic stress C5[after its division by
($ u ^ 2 (1-t ^ 2) $]and for b5 the coefficient of $ z $ in her. (After these substitutions, I would try to proceed with subsequent integrations on $ y, x, w, v, t $, integrating the additional positivity constraints C1 and C4 – which do not contain $ z $.) The normalized forms of the C2 and C5 constraints given above both have a quadratic term equal to $ -z ^ 2 $.