The Gnome's Polynomial Forest

Once upon a time, in the magical land of Gnomelandia, there was a Little Gnome. He was a curious and playful student at Gnome School. One day, during a math test on polynomials, he decided to peek at his friend's answers. Suddenly, a swirling wind surrounded him, and he was whisked away! The evil Witch appeared and cackled, "To return home, you must solve the challenges behind the eight doors in the Polynomial Forest." Add the door 2, 4, thunder, and dark door.