Question 123
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
$$
(t+3)^3 - (6t-7)^2 - (t-9)^3 \lt 3.
$$
Factor into irreducible factors with integer coefficients the expression
$$
a(x-1)x^3 + bx - 2x - 1.
$$
$$
(t+3)^3 - (6t-7)^2 - (t-9)^3 \lt 3.
$$
Factor into irreducible factors with integer coefficients the expression
$$
a(x-1)x^3 + bx - 2x - 1.
$$