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

Answer :

To solve the problem of finding the quadratic expression that represents the product of the factors [tex]\((2x + 5)(7 - 4x)\)[/tex], we can follow these steps:

1. Identify the components of each factor:
- The first factor is [tex]\(2x + 5\)[/tex].
- The second factor is [tex]\(7 - 4x\)[/tex].

2. Use the FOIL method to multiply the expressions:

- First: Multiply the first terms of each binomial.
[tex]\[
2x \times -4x = -8x^2
\][/tex]

- Outer: Multiply the outer terms.
[tex]\[
2x \times 7 = 14x
\][/tex]

- Inner: Multiply the inner terms.
[tex]\[
5 \times -4x = -20x
\][/tex]

- Last: Multiply the last terms of each binomial.
[tex]\[
5 \times 7 = 35
\][/tex]

3. Combine all the terms: Add all the results from the FOIL method together and combine like terms.

- The quadratic terms are [tex]\(-8x^2\)[/tex].
- The linear terms are [tex]\(14x - 20x\)[/tex], which combine to [tex]\(-6x\)[/tex].
- The constant term is [tex]\(35\)[/tex].

So, the quadratic expression that represents the product is:

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

Looking at the given options, the correct answer is:

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

Other Questions