Verified Answer :

  • Algebraic terms are components of an expression separated by addition or subtraction signs.
  • In the expression \(4x + 5\), the terms are \(4x\) and \(5\).
  • Since these two terms are separated by an addition sign, the total count of terms is 2.
  • The final answer is \(\boxed{2}\).

Explanation

  1. Definition of an Algebraic Term

An algebraic term is defined as a mathematical expression consisting of a single number, a single variable, or a product of numbers and variables. These terms are separated from one another by addition or subtraction operators. In the expression \(4x + 5\), we can identify the components that make up the expression by looking for these separators.

  1. Analyzing the Expression \(4x + 5\)

The expression given is \(4x + 5\). The plus sign (\(+\)) acts as a separator between two distinct components:

  1. The first component is \(4x\), which is a product of the constant 4 and the variable \(x\). This is considered a single algebraic term.
  2. The second component is \(5\), which is a constant. This is also considered a single algebraic term.

Since there is one addition operator separating these two distinct components, the expression consists of exactly two terms.

  1. Conclusion

Based on our analysis, we have identified two separate terms: \(4x\) and \(5\). Therefore, the total number of terms in the expression \(4x + 5\) is 2. This corresponds to the second option provided in the question. Thus, the correct answer is \(\boxed{2}\).

Examples

In algebra, being able to count terms is essential for simplifying complex expressions. For example, if you have a budget calculation represented by \(10x + 20y + 50\), where \(x\) represents the number of items of type A, \(y\) is the number of items of type B, and 50 is a fixed fee, you can identify that there are 3 terms contributing to your total cost. This skill helps you break down large equations into manageable parts, making it easier to perform operations like addition, subtraction, or finding the greatest common factor.