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

[tex]-2x^2 - 9x + 35[/tex]

Select the correct answer below:

A. [tex]-2x^2 - 16x + 7x + 35[/tex]

B. [tex]-2x^2 - 13x + 4x + 35[/tex]

C. [tex]-2x^2 + 5x - 8x + 35[/tex]

D. [tex]-2x^2 - 14x + 5x + 35[/tex]

E. [tex]-2x^2 + 7x - 10x + 35[/tex]

To find the correct way to group the terms of the trinomial [tex]$-2x^2 - 9x + 35$[/tex], we want to decompose the middle term [tex]$-9x$[/tex] into two terms such that their coefficients multiply to give the product of the leading coefficient [tex]$-2$[/tex] and the constant term [tex]$35$[/tex]. Let's go step-by-step through the solution:

1. Identify the product:
- Multiply the leading coefficient [tex]$-2$[/tex] by the constant term [tex]$35$[/tex]:
[tex]\[
-2 \times 35 = -70
\][/tex]

2. Find two numbers that multiply to [tex]$-70$[/tex] and add to [tex]$-9$[/tex]:
- We need two numbers that add up to [tex]$-9$[/tex] and multiply to [tex]$-70$[/tex].
- These numbers are [tex]$-14$[/tex] and [tex]$5$[/tex] because:
[tex]\[
-14 + 5 = -9 \quad \text{and} \quad -14 \times 5 = -70
\][/tex]

3. Rewrite the middle term [tex]$-9x$[/tex]:
- Replace [tex]$-9x$[/tex] with [tex]$-14x + 5x$[/tex]:
[tex]\[
-2x^2 - 9x + 35 = -2x^2 - 14x + 5x + 35
\][/tex]

4. Group and factor:
- Group the terms in pairs:
[tex]\[
(-2x^2 - 14x) + (5x + 35)
\][/tex]

- Factor each group:
- From the first group [tex]$-2x^2 - 14x$[/tex], factor out [tex]$-2x$[/tex]:
[tex]\[
-2x(x + 7)
\][/tex]
- From the second group [tex]$5x + 35$[/tex], factor out [tex]$5$[/tex]:
[tex]\[
5(x + 7)
\][/tex]

5. Combine the factored groups:
- Now, factor out the common term [tex]$(x + 7)$[/tex]:
[tex]\[
-2x(x + 7) + 5(x + 7) = (x + 7)(-2x + 5)
\][/tex]

Thus, the correct grouping is [tex]$-2x^2 - 14x + 5x + 35$[/tex]. The option that matches this grouping is:

[tex]\[
-2x^2 - 14x + 5x + 35
\][/tex]

Therefore, the correct answer is:

[tex]\[
-2x^2 - 14x + 5x + 35
\][/tex]