SEAMO 2027 - Paper F - SET 05 - Self-study Question 17

The polynomial $1-x+x^2-x^3+\cdots+x^8-x^9$ can be written as
$$a_0y^9+a_1y^8+a_2y^7+\cdots+a_8y+a_9,$$
where $x=y-1$. Find $|a_2|$.