Question

select the correct answer.
rhea is solving a math puzzle. to find the solution of the puzzle, she must find the product of two numbers. the first number is the sum of 23 and x, and the second number is 18 less than two times the first number. which of the following functions represents the product of these two numbers?
a. $p(x) = 2x^2 + 74x + 644$
b. $p(x) = 2x^2 + 110x + 1,472$
c. $p(x) = 2x^2 + 102x + 1,288$
d. $p(x) = 2x^2 + 28x - 414$

Explanation:

Step1: Define the first number

The first number is the sum of 23 and \( x \), so it can be written as \( 23 + x \).

Step2: Define the second number

The second number is 18 less than two times the first number. First, two times the first number is \( 2(23 + x) \), then subtract 18: \( 2(23 + x) - 18 \). Simplify this: \( 46 + 2x - 18 = 2x + 28 \).

Step3: Find the product of the two numbers

The product \( P(x) \) is \( (x + 23)(2x + 28) \). Use the distributive property (FOIL method):

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Answer:

A. \( P(x) = 2x^2 + 74x + 644 \)