which of the following represents a factor in the expression?

Question

24(6x+3x^2)+15

6x+3x^2
3x^2
6x
15

Answer 1

To determine which of the options represents a factor in the expression \( 24(6x + 3x^2) + 15 \), we first need to analyze the expression.

1. We can factor \( 6x + 3x^2 \): \[ 6x + 3x^2 = 3x(2 + x) \] Therefore, the term \( 24(6x + 3x^2) \) can be considered as: \[ 24 \cdot 3x(2 + x) = 72x(2 + x) \]

2. Now we look at the entire expression: \[ 24(6x + 3x^2) + 15 = 72x(2 + x) + 15 \]

Now we analyze the provided options:

• Option 1: \( 6x + 3x^2 \) is not a factor of the entire expression since it's part of a larger expression.
• Option 2: \( 3x^2 \) is also not a factor; it's part of the \( 6x + 3x^2 \).
• Option 3: \( 6x \) is also not a factor; again, it's part of the expression \( 6x + 3x^2 \).
• Option 4: \( 15 \) is just a constant term, which is also not a factor in the conventional sense.

Since none of the provided options are factors in the traditional sense of factoring the entire expression, we can conclude that none of the options represent a factor in the expression \( 24(6x + 3x^2) + 15 \).