# Ascending Order

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

## Definition

### Definition

The terms of a polynomial are in ascending order

if the exponents are increasing

as you move from the left to the right:

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

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 ascending order.

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

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

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

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

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

So +3y^{2} - 9xy + x^{2} - 4x^{3} 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 ascending order.

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

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

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

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

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