Select the best answer for the question.
3. Identify the coefficient of $-24 x^7 y^3$
A. -24
B. -3
C. 24
D. 3
Answer (2)
The problem asks to identify the coefficient of the term − 24 x 7 y 3 .
The coefficient is the numerical factor multiplying the variables.
In this case, the coefficient is − 24 .
Therefore, the answer is − 24 .
Explanation
Understanding the Problem Let's break down this problem. We are asked to identify the coefficient of the term − 24 x 7 y 3 . In algebraic terms, a coefficient is the numerical part of a term that multiplies the variables.
Identifying the Coefficient In the term − 24 x 7 y 3 , we can see that − 24 is the numerical factor that is multiplying the variables x 7 and y 3 . Therefore, the coefficient is − 24 .
Final Answer So, the coefficient of the term − 24 x 7 y 3 is − 24 .
Examples
Understanding coefficients is crucial in many real-world applications. For instance, in physics, the equation F = ma (Force equals mass times acceleration) has 'm' (mass) as the coefficient of 'a' (acceleration). Similarly, in economics, if you have a cost function C = 5 q + 100 , where 'C' is the total cost and 'q' is the quantity of goods produced, '5' is the coefficient representing the variable cost per unit. Recognizing and interpreting coefficients helps in analyzing relationships and making informed decisions in various fields.
The coefficient of the term − 24 x 7 y 3 is − 24 , which is the numerical factor in front of the variables. Therefore, the answer is option A. -24.
;
