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:
x0, x1, x2, x3, x4, x5, ... .

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 ascending order.

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

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

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

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