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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 - 34x + 35 [/tex]

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

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

Answer :

To find the product of the factors, we expand the expression:

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

Step 1: Multiply each term in the first binomial by each term in the second binomial (the FOIL method):

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

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

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

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

Step 2: Write the expression with all terms:

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

Step 3: Combine like terms (specifically the [tex]$x$[/tex] terms):

[tex]$$
14x - 20x = -6x.
$$[/tex]

Thus, the quadratic expression becomes:

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

The correct answer is:

[tex]$$\boxed{-8x^2 - 6x + 35}.$$[/tex]

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