Final answer:
Polynomial expressions are organized by the highest exponent of their variables. The expressions given are arranged from least to greatest as: iii. 8a - 5 (degree 1), i. 6x^2 (degree 2), iv. 4x^3y + 3x^2 - xy - 4 (degree 3), and ii. 18x^3 + 5ab - 6y (degree 3) based on their highest degrees.
Step-by-step explanation:
The subject of this question is organizing polynomial expressions by degree. The degree of a polynomial expression is the highest exponent of its variable(s). So, to arrange the given polynomials from least to greatest degree:
- iii. 8a - 5: This is a linear expression with a degree of 1.
- i. 6x^2: This expression has a degree of 2 since the highest exponent on the variable x is 2.
- iv. 4x^3y + 3x^2 - xy - 4: Even though it has several terms, the highest degree is 3 from the term 4x^3y.
- ii. 18x^3 + 5ab - 6y: Like the last expression, the highest degree is 3 due to the term 18x^3.
To confirm that the ordering is reasonable, we verify that each expression is organized according to its highest power of any variable present.