Hello, this problem is again from Gelfand and Shen's Algebra textbook.

Problem 171:The highest coefficient of $\displaystyle P(x)$ is 1, and we know that $\displaystyle P(1)=0, P(2)=0, P(3)=0,\ldots,P(9)=0,P(10)=0.$ What is the minimal possible degree of $\displaystyle P(x)$? Find $\displaystyle P(11)$ for this case.

Any hints would be appreaciated.