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Which of the answer choices is a correct grouping of the following trinomial?

\[ -2x^2 - 9x + 35 \]

Select the correct answer below:

A. \[ -2x^2 - 16x + 7x + 35 \]
B. \[ -2x^2 - 13x + 4x + 35 \]
C. \[ -2x^2 + 5x - 8x + 35 \]
D. \[ -2x^2 - 14x + 5x + 35 \]
E. \[ -2x^2 + 7x - 10x + 35 \]

Answer :

To solve the problem, we need to group the given trinomial [tex]\(-2x^2 - 9x + 35\)[/tex] such that when the terms are combined, they result in the original trinomial.

Here’s the step-by-step process for checking each option:

1. Option: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex]
[tex]\[
-2x^2 - 16x + 7x + 35 = -2x^2 - 9x + 35
\][/tex]
This matches the original trinomial.

2. Option: [tex]\(-2x^2 - 13x + 4x + 35\)[/tex]
[tex]\[
-2x^2 - 13x + 4x + 35 = -2x^2 - 9x + 35
\][/tex]
This also matches the original trinomial.

3. Option: [tex]\(-2x^2 + 5x - 8x + 35\)[/tex]
[tex]\[
-2x^2 + 5x - 8x + 35 = -2x^2 - 3x + 35
\][/tex]
This does not match the original trinomial.

4. Option: [tex]\(-2x^2 - 14x + 5x + 35\)[/tex]
[tex]\[
-2x^2 - 14x + 5x + 35 = -2x^2 - 9x + 35
\][/tex]
This matches the original trinomial.

5. Option: [tex]\(-2x^2 + 7x - 10x + 35\)[/tex]
[tex]\[
-2x^2 + 7x - 10x + 35 = -2x^2 - 3x + 35
\][/tex]
This does not match the original trinomial.

From this inspection, the correct answers are:
- Option 1: [tex]\(-2x^2 - 16x + 7x + 35\)[/tex]
- Option 2: [tex]\(-2x^2 - 13x + 4x + 35\)[/tex]
- Option 4: [tex]\(-2x^2 - 14x + 5x + 35\)[/tex]

Since the question asks for one correct grouping, and multiple options match the criterion, the format of the question might be misleading. However, if we strictly choose one from the provided valid options, we can say that one of these three correct answers should be accepted.

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