Question: y = 12 - x^4

Answer: Quartic binomial; down and down

Question: y = x^2 + 7 - x

Answer: quadratic trinomial; up and up; leading coefficient 1

Question: y = 2x^3 - 6x + 3x^2 - x^4 +12

Answer: quartic polynomial; down and down

Question: y = 2x^2 + 8 - 4x + x^3

Answer: cubic polynomial; down and up

Question: y = 10x^4 - 3x^3 + 3x^2 +4

Answer: quartic polynomial (not a trinomial); up and up