High School

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

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

we multiply each term in the first factor by each term in the second factor.

1. Multiply the first term in the first factor by each term in the second factor:
- [tex]\(2x \times 7 = 14x\)[/tex]
- [tex]\(2x \times (-4x) = -8x^2\)[/tex]

2. Multiply the second term in the first factor by each term in the second factor:
- [tex]\(5 \times 7 = 35\)[/tex]
- [tex]\(5 \times (-4x) = -20x\)[/tex]

3. Now, combine like terms. The [tex]\(x^2\)[/tex] term is:
[tex]$$ -8x^2 $$[/tex]

The [tex]\(x\)[/tex] terms are:
[tex]$$ 14x - 20x = -6x $$[/tex]

The constant term is:
[tex]$$ 35 $$[/tex]

So, the expanded quadratic expression is:
[tex]$$ -8x^2 - 6x + 35. $$[/tex]

Among the given options, the correct answer is:

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