Autumn tournament

Let $a$ be the largest value of the expression $24y-9y^2$, where $y$ is a rational number and $b$ is the smallest integer satisfying the inequality $$(t+3{)}^3-(6t-7{)}^2-(t-9{)}^3<3.$$ Factor into irreducible factors with integer coefficients the expression $$a(x-1)x^3+bx-2x-1.$$