I2.1 If $a^{2}-1=123 \times 125$ and $a>0$, find $a$.
I2.2 If the remainder of $x^{3}-16 x^{2}-9 x+a$ when divided by $x-2$ is $b$, find $b$.
I2.3 If an $n$-sided polygon has $(b+4)$ diagonals, find $n$.
I2.4 If the points $(3, n),(5,1)$ and $(7, d)$ are collinear, find $d$.
$\begin{array}{l}a^{2}-1=(124-1) \times(124+1) \\ \quad=124^{2}-1 \\ a=124 \\ b=2^{3}-16(2)^{2}-9(2)+124=50 \\ C_{2}^{n}-n=50+4 \\ n(n-3)=108 \\ n^{2}-3 n-108=0 \\ (n-12)(n+9)=0 \\ \Rightarrow n=12 \\ \frac{12-1}{3-5}=\frac{d-1}{7-5} \\ d-1=-11 \\ \Rightarrow d=-10\end{array}$