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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 + 6x - 35 [/tex]

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

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

Answer :

Sure! Let's find the product of the given factors step-by-step:

The factors are [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex].

### Step-by-Step Solution

1. Distribute each term in the first factor by each term in the second factor:

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

2. Use the distributive property (also known as the FOIL method for binomials):
- First: [tex]\(2x \cdot 7 = 14x\)[/tex]
- Outer: [tex]\(2x \cdot (-4x) = -8x^2\)[/tex]
- Inner: [tex]\(5 \cdot 7 = 35\)[/tex]
- Last: [tex]\(5 \cdot (-4x) = -20x\)[/tex]

3. Combine all the products:

[tex]\[
14x + (-8x^2) + 35 + (-20x)
\][/tex]

4. Combine like terms:

[tex]\[
-8x^2 + 14x - 20x + 35
\][/tex]

Simplify the [tex]\(x\)[/tex]-terms:

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

### Conclusion
The quadratic expression that represents the product of [tex]\((2x + 5)(7 - 4x)\)[/tex] is:

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

So, the correct answer is:

A. [tex]\(-8x^2 - 6x + 35\)[/tex]

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