descending order

Descending order means arranging a polynomial's terms from the highest power down to the lowest, like stairs going down: the x^4 term first, then x^3, then x^2, then x, then the constant. It is the convention behind the standard form of a polynomial.

Writing in descending order is not just neatness — it makes every later step easier. The first term immediately reveals the degree and the leading coefficient, and both long division and synthetic division assume the terms are lined up this way before you begin.

The opposite arrangement, lowest power first, is called ascending order and shows up in calculus and power series. For ordinary algebra, though, descending order is the default; whenever you finish simplifying, sort your answer this way as a final tidy-up.