Let the polynomial \( P(x) = x^4 + ax^3 + bx + 1 \) with \( a, b \in \mathbb{R} \). Find \( a \) and \( b \) such that \( P(x) \) is divisible by \((x + 1)^2\).

Exercise 2:

What is the remainder of the Euclidean division of:

\[P(x) = (x - 2)^{2n} + (x - 1)^n - 2\]

by:

1. \( x^2 - 3x + 2 \)
2. \( x^2 - 2x + 1 \)