[Bezout's Theorem. Factorization]

For what values of the parameter $a$ does the polynomial $P(x)=x^{n}+a x^{n-2}(n \geq 2)$ divide by $x-2$?
$P(2)=2^{n}+a \cdot 2^{n-2}=2^{n-2}(4+a)$.

## Answer

For $a=-4$.