\(F\left(x-3\right).F\left(x-1\right)=x.F\left(x+5\right)\left(1\right)\)
\(TH_1:x=0;\left(1\right)\Rightarrow F\left(-3\right).F\left(-1\right)=0\Rightarrow\left[{}\begin{matrix}F\left(-3\right)=0\\F\left(-1\right)=0\end{matrix}\right.\)
\(\Rightarrow F\left(x\right)\) có ít nhất \(2\) nghiệm \(x=-1;x=-3\)
\(TH_2:x=3;\left(1\right)\Rightarrow F\left(0\right).F\left(2\right)=3.F\left(8\right)\)
\(TH_3:x=1;\left(1\right)\Rightarrow F\left(-2\right).F\left(0\right)=F\left(6\right)\)
\(\Rightarrow\)\(F\left(8\right)=0\cup F\left(6\right)=0\) nếu \(F\left(0\right)=0\)
\(TH_4:x=-5;\left(1\right)\Rightarrow F\left(-8\right).F\left(-6\right)=-5.F\left(0\right)\)
\(\Rightarrow F\left(-8\right)=0\cup F\left(-6\right)=0\) nếu \(F\left(0\right)=0\)
Vậy \(F\left(x\right)\) có ít nhất \(4\) nghiệm (đpcm)
