I5.2 Let $f(x)=x^{3}-20 x^{2}+x-a$ and $g(x)=x^{4}+3 x^{2}+2$. If $h(x)$ is the highest common factor of $f(x)$ and $g(x)$, find $b=h(1)$.
Reference: 1992 HI5
$$
\begin{array}{l}
f(x)=x^{3}-20 x^{2}+x-20=\left(x^{2}+1\right)(x-20) \\
g(x)=x^{4}+3 x^{2}+2=\left(x^{2}+1\right)\left(x^{2}+2\right) \\
h(x)=\text { H.C.F. }=x^{2}+1 \\
b=h(1)=2
\end{array}
$$