Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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 - 34x + 35[/tex]
D. [tex]-8x^2 + 6x - 35[/tex]

To find the product of the factors

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

we apply the distributive property (also known as the FOIL method). Here are the steps:

1. Multiply the first term of the first factor by each term of the second factor:
- [tex]$$ 2x \cdot 7 = 14x $$[/tex]
- [tex]$$ 2x \cdot (-4x) = -8x^2 $$[/tex]

2. Multiply the second term of the first factor by each term of the second factor:
- [tex]$$ 5 \cdot 7 = 35 $$[/tex]
- [tex]$$ 5 \cdot (-4x) = -20x $$[/tex]

3. Combine the like terms (the [tex]$x$[/tex] terms):
- From step 1 and step 2, the [tex]$x$[/tex] terms are: [tex]$$ 14x \text{ and } -20x $$[/tex]
- Adding them gives: [tex]$$ 14x - 20x = -6x $$[/tex]

4. Write the final expanded quadratic expression:
- The [tex]$x^2$[/tex] term is: [tex]$$ -8x^2 $$[/tex]
- The [tex]$x$[/tex] term is: [tex]$$ -6x $$[/tex]
- The constant term is: [tex]$$ 35 $$[/tex]

Thus, the product is:

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

Comparing with the given options, we see that option A is:

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

So, the correct answer is option A.