I4.1 If each interior angle of a $n$-sided regular polygon is $140^{\circ}$, find $n$.
I4.2 If the solution of the inequality $2 x^{2}-n x+9<0$ is $k<x<b$, find $b$.
I4.3 If $c x^{3}-b x+x-1$ is divided by $x+1$, the remainder is -7 , find $c$.
I4.4 If $x+\frac{1}{x}=c$ and $x^{2}+\frac{1}{x^{2}}=d$, find $d$.
Each exterior angle is $40^{\circ}$ (adj. $\angle$ s on st. line)
$$
\begin{array}{l}
\frac{360^{\circ}}{n}=40^{\circ} \\
n=9 \\
2 x^{2}-9 x+9<0 \\
(2 x-3)(x-3)<0 \\
\frac{3}{2}<x<3 \\
\Rightarrow b=3 \\
f(x)=c x^{3}-3 x+x-1 \\
f(-1)=-c+3-1-1=-7 \\
c=8 \\
x+\frac{1}{x}=8 \\
\Rightarrow\left(x+\frac{1}{x}\right)^{2}=64 \\
x^{2}+\frac{1}{x^{2}}+2=64 \\
d=62
\end{array}
$$