4. Let the polynomial $f(x)=a_{0} x^{4}+a_{1} x^{3}+a_{2} x^{2}+a_{3} x+a_{4}$. If $f(1)=f(2)=f(3)=0, f(4)=6, f(5)=72$, find $f(x)$.
(Tip: By the factor theorem, let $f(x)=(x-1)(x-2)$ $(x-3)(a x+b)$. Then $f(4)=3 \times 2 \times 1 \times(4 a+b)=6$, $f(5)=4 \times 3 \times 2 \times(5 a+b)=72$. Solving yields $a=2, b=$ -7.)