Select the correct answer.
Write an expression to represent the product of 6 and the square of a number plus 15. In your expression, what is the value of the coefficient?
A. 1
B. 15
C. 2
D. 6
Answer (1)
Represent the unknown number with a variable: x .
Express the square of the number: x 2 .
Add 15 to the square: x 2 + 15 .
Multiply the entire expression by 6 and distribute: 6 ( x 2 + 15 ) = 6 x 2 + 90 . The coefficient of x 2 is 6 .
Explanation
Understanding the Problem Let's break down the problem step by step to create the correct expression and identify the coefficient.
Representing the Number Let's use x to represent the unknown number.
Squaring the Number The square of the number is then x 2 .
Adding 15 Adding 15 to the square of the number gives us x 2 + 15 .
Multiplying by 6 Finally, we multiply the entire expression by 6: 6 ( x 2 + 15 ) .
Distributing Distributing the 6, we get 6 x 2 + 6 × 15 = 6 x 2 + 90 .
Identifying the Coefficient In the expression 6 x 2 + 90 , the coefficient is the number multiplying the variable x 2 , which is 6.
Final Answer Therefore, the correct answer is D. 6.
Examples
Understanding coefficients and expressions is crucial in many real-world applications. For example, if you're calculating the area of a rectangular garden where the length is dependent on a variable (like the square of a number) and you need to scale the fertilizer needed (multiplying by a constant), this type of expression helps determine the total amount of fertilizer required. Similarly, in physics, understanding coefficients in equations helps in calculating forces or energies based on certain variables.
