Select the best answer for the question. Identify the coefficient of [tex]$17 x y^3 z^{12}$[/tex]
A. 3
B. 17
C. 1
D. 12
Answer (2)
The coefficient of a term is the numerical factor multiplying the variable part of the term.
In the term 17 x y 3 z 12 , the numerical factor is 17.
Therefore, the coefficient is 17.
The answer is 17 .
Explanation
Understanding the Problem We are asked to identify the coefficient of the term 17 x y 3 z 12 . The coefficient is the numerical factor that multiplies the variable part of the term.
Identifying the Coefficient In the term 17 x y 3 z 12 , the numerical factor is 17. Therefore, the coefficient is 17.
Final Answer The coefficient of the term 17 x y 3 z 12 is 17.
Examples
In algebra, identifying coefficients is crucial for understanding the structure of expressions and solving equations. For instance, when analyzing a polynomial representing the trajectory of a ball, the coefficient of the t 2 term (where t is time) tells us about the acceleration due to gravity. Similarly, in financial models, coefficients in regression equations help quantify the impact of different factors on an outcome, such as the effect of advertising spend on sales. Understanding coefficients allows us to interpret and manipulate mathematical models effectively in various real-world applications.
The coefficient of the term 17 x y 3 z 12 is 17 . Thus, the correct option is B. 17.
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