The remainder when 𝑝(𝑥) = 𝑥^2022 − 𝑥^2021 + 𝑥^2020 − ⋯ + (−1)^𝑖𝑥^𝑖 + ⋯ −𝑥^3 + 𝑥^2 − 𝑥 + 1, is divided by (𝑥 − 1) is

Answer 1

when 𝑝(𝑥) = 𝑥^2022 − 𝑥^2021 + 𝑥^2020 − ⋯ + (−1)^𝑖𝑥^𝑖 + ⋯ −𝑥^3 + 𝑥^2 − 𝑥 + 1 is divided by x-1 the remainder is f(1)
f(1) = 1^2022 - 1^2021 + .....+ 1^2 - 1^1 + 1
= (1^2022 - 1^2021) + .....+ (1^2 - 1^1) + 1

each pair is zero, so f(1) = ....