Question
Which of the following includes a coefficient? A \( 3 x+2 \) B \( a^{2}-.1 \)
Ask by Stuart Williams. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A \( 3x + 2 \) includes a coefficient.
Solution
To determine which of the given expressions includes a coefficient, we need to understand what a coefficient is. A coefficient is a numerical factor that multiplies a variable in an algebraic expression.
Let's analyze each option:
A. \( 3x + 2 \)
- In this expression, \( 3 \) is the coefficient of the variable \( x \).
B. \( a^{2} - 0.1 \)
- In this expression, there is no coefficient multiplying the variable \( a^{2} \). The term \( -0.1 \) is a constant, not a coefficient of \( a^{2} \).
Based on this analysis, the expression that includes a coefficient is:
**A \( 3x + 2 \)**.
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Simplify this solution Beyond the Answer
In the expression \( 3x + 2 \), the number 3 is a coefficient that multiplies the variable \( x \). Coefficients are the numerical factors in terms, which help determine the scaling of the variable. In contrast, the expression \( a^{2} - 0.1 \) does not include a coefficient in front of \( a^{2} \); rather, 0.1 is a constant. Keep in mind that coefficients can be more than just whole numbers. They can be fractions, decimals, or even negative numbers, so keep an eye out for them when working with algebraic expressions!
