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

Answer :

To find the product of the factors [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex], we can use the distributive property, also known as the FOIL method for binomials. Here's how it works step-by-step:

1. First: Multiply the first terms of each factor:
[tex]\[
2x \cdot 7 = 14x
\][/tex]

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

3. Inner: Multiply the inner terms:
[tex]\[
5 \cdot 7 = 35
\][/tex]

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

Now, combine all these results:
[tex]\[
14x + (-8x^2) + 35 + (-20x)
\][/tex]

Next, let's simplify by combining like terms:
- Combine the [tex]\(x\)[/tex] terms: [tex]\(14x - 20x = -6x\)[/tex]

So, the quadratic expression simplifies to:
[tex]\[
-8x^2 - 6x + 35
\][/tex]

Therefore, the quadratic expression representing the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex] is:
- [tex]\(-8x^2 - 6x + 35\)[/tex]

The correct answer is C. [tex]\(-8x^2 - 6x + 35\)[/tex].

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