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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 - 6x + 35[/tex]

B. [tex]-8x^2 + 34x - 35[/tex]

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

D. [tex]-8x^2 - 34x + 35[/tex]

To solve the problem, we need to find the product of the two factors:

[tex]$$
(2x+5)(7-4x)
$$[/tex]

Step 1. Multiply the first term of the first factor by each term of the second factor:

- Multiply [tex]$2x$[/tex] by [tex]$7$[/tex]:
[tex]$$
2x \cdot 7 = 14x
$$[/tex]

- Multiply [tex]$2x$[/tex] by [tex]$-4x$[/tex]:
[tex]$$
2x \cdot (-4x) = -8x^2
$$[/tex]

Step 2. Multiply the second term of the first factor by each term of the second factor:

- Multiply [tex]$5$[/tex] by [tex]$7$[/tex]:
[tex]$$
5 \cdot 7 = 35
$$[/tex]

- Multiply [tex]$5$[/tex] by [tex]$-4x$[/tex]:
[tex]$$
5 \cdot (-4x) = -20x
$$[/tex]

Step 3. Combine all the terms:

Write down all the products:
[tex]$$
-8x^2 + 14x - 20x + 35
$$[/tex]

Combine like terms ([tex]$14x - 20x$[/tex]):
[tex]$$
-8x^2 - 6x + 35
$$[/tex]

This quadratic expression represents the product of the factors.

Step 4. Select the Correct Option:

Comparing with the options given:

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

We see that the expression we found [tex]$(-8x^2 - 6x + 35)$[/tex] matches option A.

Thus, the correct answer is Option A.