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

Answer :

Factoring

To find the product of the factors [tex](2x + 5)(7 - 4x)[/tex], we use the FOIL method (First, Outer, Inner, Last):

First: [tex](2x)(7) = 14x[/tex]

Outer: [tex](2x)(-4x) = -8x^2[/tex]

Inner: [tex](5)(7) = 35[/tex]

Last: [tex](5)(-4x) = -20x[/tex]

Combine the terms:

[tex]14x - 8x^2 + 35 - 20x = -8x^2 - 6x + 35[/tex]

Final answer:

  • Therefore, the correct quadratic expression is A. -8x² - 6x + 35

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