# 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:

x^{5}, x^{4}, x^{3}, x^{2}, x^{1}, x^{0}, ... .

x^{0} term is the constant term: the term that don't have x.

(x^{0} = 1)

## Example 1

### Example

### Solution

Find the powers of x in the given terms.

x^{2} has x^{2}.

+3y^{2} doesn't have x.

So it's the x^{0} term.

-9xy has x^{1}.

-4x^{3} has x^{3}.

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

First write the x^{3} term: -4x^{3}.

Write the x^{2} term: +x^{2}.

Write the x^{1} term: -9xy.

And write the remaining x^{0} term: +3y^{2}.

The powers of x are in descending order: x^{3}, x^{2}, x^{1}, x^{0}.

So -4x^{3} + x^{2} - 9xy + 3y^{2} is the answer.

## Example 2

### Example

### Solution

Find the powers of y in the given terms.

x^{2} doesn't have y.

So it's the y^{0} term.

+3y^{2} has y^{2}.

-9xy has y^{1}.

-4x^{3} doesn't have y.

So it's also the y^{0} term.

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

First write the y^{2} term: 3y^{2}.

Write the y^{1} term: -9xy.

And write the remaining y^{0} terms: -4x^{3} + x^{2}.

The powers of y are in descending order: y^{2}, y^{1}, y^{0}, y^{0}.

So 3y^{2} - 9xy - 4x^{3} + x^{2} is the answer.