I1.2 Given that $f(x)=x^{2}+a x+b$ is the common factor of $x^{3}+4 x^{2}+5 x+6$ and $2 x^{3}+7 x^{2}+9 x+10$ If $f(P)=Q$, find the value of $Q$.
Let $g(x)=x^{3}+4 x^{2}+5 x+6 ; h(x)=2 x^{3}+7 x^{2}+9 x+10$
$g(-3)=-27+36-15+6=0,(x+3)$ is a factor of $g(x)$; by division, $g(x)=(x+3)\left(x^{2}+x+2\right)$
$h(-2.5)=-31.25+43.75-22.5+10=0,(2 x+5)$ is a factor of $h(x)$; by division, $h(x)=(2 x+5)\left(x^{2}+x+2\right)$
$f(x)=$ common factor $=\left(x^{2}+x+2\right)$
$Q=f(P)=f(1)=1+1+2=4$