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------------------------------------------------ Select the correct answer.

The product of two integers is 112. One number is four more than three times the other. Which of the following equations could be used to find one of the numbers?

A. [tex]3x^2 + 4x = 112[/tex]
B. [tex]3x^2 + 4 = 112[/tex]
C. [tex]4x^2 + 3x = 112[/tex]
D. [tex]4x^2 + 3 = 112[/tex]

To solve this problem, we need to find the correct equation that represents the relationship given in the problem between two integers.

Let's break down the information:

1. We have two integers. Let's call one integer [tex]\( x \)[/tex].

2. According to the problem, the other integer is "four more than three times" the first integer. In mathematical terms, this can be expressed as [tex]\( 3x + 4 \)[/tex].

3. The product of these two integers is 112.

Now, let's formulate the equation:
- The product of the integers can be expressed as:
[tex]\[
x \times (3x + 4) = 112
\][/tex]

- Expanding the left side, we have:
[tex]\[
x \times (3x + 4) = 3x^2 + 4x
\][/tex]

- Therefore, the equation becomes:
[tex]\[
3x^2 + 4x = 112
\][/tex]

This matches option A, which is [tex]\( 3x^2 + 4x = 112 \)[/tex].

So, the correct answer is option A.