Descending Order

How to arrange the terms of a polynomial in descending order: definition, 2 examples, and their solutions.

Definition

Definition

The terms of a polynomial are in descending order
if the exponents are decreasing
as you move from the left to the right:
x5, x4, x3, x2, x1, x0, ... .

x0 term is the constant term: the term that don't have x.
(x0 = 1)

Example 1

Example

Solution

Find the powers of x in the given terms.

x2 has x2.

+3y2 doesn't have x.
So it's the x0 term.

-9xy has x1.

-4x3 has x3.

See the exponents of x and arrange the terms in descending order.

First write the x3 term: -4x3.
Write the x2 term: +x2.
Write the x1 term: -9xy.
And write the remaining x0 term: +3y2.

The powers of x are in descending order: x3, x2, x1, x0.
So -4x3 + x2 - 9xy + 3y2 is the answer.

Example 2

Example

Solution

Find the powers of y in the given terms.

x2 doesn't have y.
So it's the y0 term.

+3y2 has y2.

-9xy has y1.

-4x3 doesn't have y.
So it's also the y0 term.

See the exponents of y and arrange the terms in descending order.

First write the y2 term: 3y2.
Write the y1 term: -9xy.
And write the remaining y0 terms: -4x3 + x2.

The powers of y are in descending order: y2, y1, y0, y0.
So 3y2 - 9xy - 4x3 + x2 is the answer.