1. The quadratic trinomial $a x^{2}+b x+c$, for $x=1 ; 2 ; 3$, takes values $0 ; 1 ; 4$ respectively. What value does this polynomial take for $x=11$?
Solution. From the conditions of the problem, the following system of linear equations with unknowns $a, b, c$ is obtained:

$$
\left\{\begin{array}{l}
a+b+c=0 \\
4 a+2 b+c=1 \\
9 a+3 b+c=4
\end{array}\right.
$$

Solving this system, we get $a=1, c=1, b=-2$, so the given polynomial is $x^{2}-2 x+1$. If we substitute $x=11$ into the obtained polynomial, we get that the desired value is 100.