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

Which quadratic expression represents the product of these factors?
[tex]$(2x + 5)(7 - 4x)$[/tex]

A. [tex]$-8x^2 - 34x + 35$[/tex]
B. [tex]$-8x^2 + 34x - 35$[/tex]
C. [tex]$-8x^2 + 6x - 35$[/tex]
D. [tex]$-8x^2 - 6x + 35$[/tex]

To solve for the product of the quadratic expression [tex]$(2x + 5)(7 - 4x)$[/tex], let's multiply these two binomials using the distributive property, often remembered as the FOIL method, which stands for First, Outer, Inner, Last:

1. First terms: Multiply the first terms of each binomial:
- [tex]$2x \times 7 = 14x$[/tex]

2. Outer terms: Multiply the outer terms of the binomials:
- [tex]$2x \times (-4x) = -8x^2$[/tex]

3. Inner terms: Multiply the inner terms of the binomials:
- [tex]$5 \times 7 = 35$[/tex]

4. Last terms: Multiply the last terms of each binomial:
- [tex]$5 \times (-4x) = -20x$[/tex]

Now, we need to combine all these results:

- Start with the [tex]$-8x^2$[/tex].
- The x terms [tex]$14x - 20x = -6x$[/tex].
- Lastly, add the constant term [tex]$35$[/tex].

Putting it all together, the quadratic expression is:

[tex]\[ -8x^2 - 6x + 35 \][/tex]

Therefore, the correct choice is D: [tex]$-8x^2 - 6x + 35$[/tex].