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------------------------------------------------ Multiply the polynomials:

[tex]
(5x^2 + 2x + 8)(7x - 6)
[/tex]

A. [tex]35x^3 - 16x^2 + 44x + 48[/tex]

B. [tex]35x^3 - 16x^2 - 44x - 48[/tex]

C. [tex]35x^3 - 14x^2 + 44x - 48[/tex]

D. [tex]35x^3 - 16x^2 + 44x - 48[/tex]

To multiply the polynomials [tex]$(5x^2 + 2x + 8)(7x - 6)$[/tex], we will use the distributive property (also known as the FOIL method for binomials). Let's break it down step-by-step:

1. Multiply each term in the first polynomial by each term in the second polynomial:

- Multiply [tex]$5x^2$[/tex] by each term in [tex]$7x - 6$[/tex]:
- [tex]$5x^2 \times 7x = 35x^3$[/tex]
- [tex]$5x^2 \times -6 = -30x^2$[/tex]

- Multiply [tex]$2x$[/tex] by each term in [tex]$7x - 6$[/tex]:
- [tex]$2x \times 7x = 14x^2$[/tex]
- [tex]$2x \times -6 = -12x$[/tex]

- Multiply [tex]$8$[/tex] by each term in [tex]$7x - 6$[/tex]:
- [tex]$8 \times 7x = 56x$[/tex]
- [tex]$8 \times -6 = -48$[/tex]

2. Combine all the products:
- [tex]$35x^3$[/tex]
- [tex]$-30x^2 + 14x^2 = -16x^2$[/tex] (Combine the [tex]$x^2$[/tex] terms)
- [tex]$-12x + 56x = 44x$[/tex] (Combine the [tex]$x$[/tex] terms)
- [tex]$-48$[/tex]

3. Combine all these terms to form the final polynomial:
[tex]\[
35x^3 - 16x^2 + 44x - 48
\][/tex]

So, the multiplied result of the polynomials is:
[tex]\[
35x^3 - 16x^2 + 44x - 48
\][/tex]

Therefore, the correct answer is option D: [tex]$35x^3 - 16x^2 + 44x - 48$[/tex].