Certainly! Let's analyze the expression [tex]\( 5x + 2^3 \)[/tex] and match the vocabulary words accordingly, step by step.
First, let's break down the expression into its components:
1. Term 1: [tex]\( 5x \)[/tex]
- Coefficient: In the term [tex]\( 5x \)[/tex], the number directly multiplying the variable [tex]\( x \)[/tex] is 5. Hence, the coefficient here is 5.
- Variable: The variable in the term [tex]\( 5x \)[/tex] is [tex]\( x \)[/tex].
2. Term 2: [tex]\( 2^3 \)[/tex]
- Base: In the exponential expression [tex]\( 2^3 \)[/tex], the base is 2.
- Exponent: The exponent in the expression [tex]\( 2^3 \)[/tex] is 3.
Given this breakdown, let’s match the vocabulary words correctly:
1. 2
- This refers to the base in the expression [tex]\( 2^3 \)[/tex].
- Therefore, 2 matches with base.
2. 3
- This refers to the exponent in the expression [tex]\( 2^3 \)[/tex].
- Thus, 3 matches with exponent.
3. 5
- This refers to the coefficient in the term [tex]\( 5x \)[/tex].
- Hence, 5 matches with coefficient.
4. [tex]\( x \)[/tex]
- This refers to the variable in the term [tex]\( 5x \)[/tex].
- Thus, [tex]\( x \)[/tex] matches with variable.
Now, let’s summarize the correct matching:
- The number 2 matches with base.
- The number 3 matches with exponent.
- The number 5 matches with coefficient.
- The variable [tex]\( x \)[/tex] matches with variable.
Therefore, the correct matches are:
1. 2 → base
2. 3 → exponent
3. 5 → coefficient
4. [tex]\( x \)[/tex] → variable
