College

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 :

Let's work through the problem of finding the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex] step-by-step, using the distributive property (also known as the FOIL method for binomials).

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

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

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

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

5. Combine all these results together:
[tex]\[-8x^2 + 14x + 35 - 20x\][/tex]

6. Combine like terms:
[tex]\[14x - 20x = -6x\][/tex]

So, the quadratic expression formed by multiplying the given factors is:
[tex]\[-8x^2 - 6x + 35\][/tex]

Therefore, the correct answer from the multiple-choice options is:
[tex]\[C. -8x^2 - 6x + 35\][/tex]