Ascending Order, Descending Order

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

Arrange the terms of the given polynomial so that the powers of x are in ascending order. x^2 + 3y^2 - 9xy + 7 - 4x^3

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 (= x0):
3y2 + 7.

Write the x term (= x1):
-9xy.

Write the x2 term:
+x2.

Write the x3 term:
-4x3.

Example 2

Arrange the terms of the given polynomial so that the powers of x are in descending order. x^2 + 3y^2 - 9xy + 7 - 4x^3

Descending order looks like this: 3, 2, 1, 0.
So start writing from the greater powers of x.

Write the x3 term:
-4x3.

Write the x2 term:
+x2.

Write the x term (= x1):
-9xy.

Write the terms that don't have x (= x0):
+3y2 + 7.

Example 3

Arrange the terms of the given polynomial so that the powers of y are in ascending order. x^2 + 3y^2 - 9xy + 7 - 4x^3

Start writing from the lesser powers of y.

Write the terms that don't have y (= y0):
-4x3 + x2 + 7.

Write the y term (= y1):
-9xy.

Write the y2 term:
+3y2.

Example 4

Arrange the terms of the given polynomial so that the powers of y are in descending order. x^2 + 3y^2 - 9xy + 7 - 4x^3

Start writing from the greater powers of y.

Write the y2 term:
+3y2.

Write the y term (= y1):
-9xy.

Write the terms that don't have y (= y0):
-4x3 + x2 + 7.