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13 problems match “factoring”. Clear

Value of f(2) for a quadratic ●●●○○ 50 ptsLet $a$ and $b$ be real numbers. The quadratic function $f(x)=x^{2}+ax+b$ satisfies $f(f(0))=f(f(1))=0$ and $f(0)\neq f(1)$ . Find $f(2)$ .
Largest edge of a box ●●●○○ 50 ptsAn $m\times n\times p$ rectangular box has half the volume of an $(m + 2)\times(n + 2)\times(p + 2)$ rectangular box, where $m, n,$ and $p$ are positive integers with $m\le n\le p$ . Find the largest possible value of $p$ .
Common ratio from a sum relation ●●●○○ 50 ptsLet $S_n$ be the sum of the first $n$ terms of a geometric sequence $\{a_n\}$ with nonzero first term and common ratio $q$ . Given that $S_4 = 5S_2$ , find all possible values of $q$ , listed in increasing order.