1. Find the sum of the coefficients of the polynomial obtained after expanding the brackets and combining like terms in the expression

$\left(2 x^{2021}-x^{2020}+x^{2019}\right)^{11}-29$.
Solution. First, note that the sum of the coefficients of any polynomial in canonical form $P(x)=a_{0} x^{n}+a_{1} x^{n-1}+\ldots+a_{n-1} x+a_{n}$ is $P(1)$. Next, note that after raising the bracket to the 11th power, the polynomial $Q(x)=\left(2 x^{2021}-x^{2020}+x^{2019}\right)^{11}-29$ will take a canonical form (some of the coefficients may turn out to be zero). Thus, the sum of the coefficients of the polynomial $Q(x)$ is $Q(1)=2^{11}-29=$ 2019. Answer: 2019.

Comment. Solutions in which the value of the polynomial at the point 1 appears in some form are scored full marks. For example, “It is obvious that the sum of the coefficients of the polynomial is equal to its value at the point 1. Answer: 2019.” or $\ll Q(1)=2019 »$. Only the correct answer is given - 3 points.