[tex]xP(x-1)=(x-3)P(x) \\ \\ x=1:\quad P(0) = -2P(1) \\ x=2:\quad 2P(1) = -P(2) \\ x=3: \quad 3P(2) = 0 \Rightarrow P(2) = 0 \Rightarrow P(1) = 0 \Rightarrow P(0) = 0 \\ \\ P(x) \text{ are coeficientul dominant 1 }\Rightarrow a_{n} = 1 \\ \\ P(x) = x^n+a_{n-1}x^{n-1}+...+a_1x+a_0 = a(x-x_1)(x-x_2)\cdot...\cdot(x-x_n),\quad a = 1\\ \\ \text{Sa zicem ca P(x) ar fi }x(x-1)(x-2)}[/tex]
[tex]P(x-1) = (x-1)(x-2)(x-3)\\ xP(x-1) = x(x-1)(x-2)(x-3) \\ xP(x-1) = P(x)\cdot (x-3) \\ \\ xP(x-1) = (x-3)P(x) \\ \\ \Rightarrow P(x) = x(x-1)(x-2) \\ \\ \Rightarrow P(5) = 5\cdot 4\cdot 3 = 60[/tex]
