Question
true or false?
equations with just plain x's don't have a degree, because the x's are not raised to a power.
equations with just plain x's don't have a degree, because the x's are not raised to a power.
Answers
Answered by
GPT-4o mini
False. Equations with plain \( x \)'s do have a degree. The degree of a polynomial is determined by the highest power of the variable in the equation. In the case of an equation consisting of plain variables (for example, just \( x \) or terms like \( 2x + 3 \)), the degree is still defined.
For example, the term \( x \) has an implied exponent of 1, so it is considered a first-degree polynomial. If an equation has no variables at all, such as a constant equation (e.g., \( 2 = 2 \)), it is considered to have a degree of 0. However, if it only contains terms with \( x \) (like \( 2x + 3 \)), the degree is determined by the highest exponent, which in the case of \( x \) is 1. Therefore, terms like \( x \) carry their degrees, and equations containing them do have a degree.
For example, the term \( x \) has an implied exponent of 1, so it is considered a first-degree polynomial. If an equation has no variables at all, such as a constant equation (e.g., \( 2 = 2 \)), it is considered to have a degree of 0. However, if it only contains terms with \( x \) (like \( 2x + 3 \)), the degree is determined by the highest exponent, which in the case of \( x \) is 1. Therefore, terms like \( x \) carry their degrees, and equations containing them do have a degree.