Question

Which of the following expressions can be compared to 3x2+15x−42x2−4 , and is also an equivalent form?(1 point) Responses 3(x+7) 3 left parenthesis x plus 7 right parenthesis 3(5x−12)−4 Start Fraction 3 left parenthesis 5 x minus 12 right parenthesis over negative 4 End Fraction (3x+21)(x−2)x+2 Start Fraction left parenthesis 3 x plus 21 right parenthesis left parenthesis x minus 2 right parenthesis over x plus 2 End Fraction 3(x+7)x+2 Start Fraction 3 left parenthesis x plus 7 right parenthesis over x plus 2 End Fraction

Answer 1

To determine which expression can be compared to \( 3x^2 + 15x - 42x^2 - 4 \) and is equivalent, we first need to simplify the given polynomial.

Starting with the expression:

\[
3x^2 + 15x - 42x^2 - 4
\]

We can combine like terms:

1. Combine the \( x^2 \) terms:
\[
3x^2 - 42x^2 = -39x^2
\]

2. The \( x \) term remains \( 15x \).

3. The constant term remains \( -4 \).

Putting it all together, we find:

\[
-39x^2 + 15x - 4
\]

Now, let's evaluate the options provided to see which one is equivalent to this expression.

### Option 1: \( 3(x+7) \)

Expanding \( 3(x + 7) \):
\[
3x + 21
\]
This does not match \( -39x^2 + 15x - 4 \).

### Option 2: \( 3(5x - 12) - 4 \)

Expanding this gives:
\[
3(5x - 12) - 4 = 15x - 36 - 4 = 15x - 40
\]
This does not match \( -39x^2 + 15x - 4 \).

### Option 3: \( (3x + 21)(x - 2) \)

Expanding this gives:
\[
3x^2 - 6x + 21x - 42 = 3x^2 + 15x - 42
\]
This does not match our expression.

### Option 4: \( \frac{3(x + 7)}{x + 2} \)

This form does not have the appropriate degree to match \( -39x^2 + 15x - 4 \).

Since none of these simplifications and comparisons have yielded an equivalent form to \( -39x^2 + 15x - 4 \), please check if I have correctly interpreted the original polynomial and if the provided options are indeed exhaustive lists. If you need further evaluation or a different approach, let me know!