# Ascending Order, Descending Order

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

## Example 1

Ascending order looks like this: 0, 1, 2, 3, ... .

So start writing from the lesser powers of *x*.

Write the terms that don't have *x* (= *x*^{0}):

3*y*^{2} + 7.

Write the *x* term (= *x*^{1}):

-9*xy*.

Write the *x*^{2} term:

+*x*^{2}.

Write the *x*^{3} term:

-4*x*^{3}.

## Example 2

Descending order looks like this: 3, 2, 1, 0.

So start writing from the greater powers of *x*.

Write the *x*^{3} term:

-4*x*^{3}.

Write the *x*^{2} term:

+*x*^{2}.

Write the *x* term (= *x*^{1}):

-9*xy*.

Write the terms that don't have *x* (= *x*^{0}):

+3*y*^{2} + 7.

## Example 3

Start writing from the lesser powers of *y*.

Write the terms that don't have *y* (= *y*^{0}):

-4*x*^{3} + *x*^{2} + 7.

Write the *y* term (= *y*^{1}):

-9*xy*.

Write the *y*^{2} term:

+3*y*^{2}.

## Example 4

Start writing from the greater powers of *y*.

Write the *y*^{2} term:

+3*y*^{2}.

Write the *y* term (= *y*^{1}):

-9*xy*.

Write the terms that don't have *y* (= *y*^{0}):

-4*x*^{3} + *x*^{2} + 7.