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

Answer :

Sure! Let's find the quadratic expression representing the product of the factors [tex]\((2x + 5)\)[/tex] and [tex]\((7 - 4x)\)[/tex].

To do this, we'll use the distributive property, often remembered as the FOIL method, which stands for First, Outer, Inner, Last.

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

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

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

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

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

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

Therefore, the quadratic expression is [tex]\(-8x^2 - 6x + 35\)[/tex].

This matches option C in the list:
[tex]\[
\text{C. } -8x^2 - 6x + 35
\][/tex]

So, the correct answer is option C.

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