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

[tex]\left(7x^2 + 5x + 7\right)(4x - 6)[/tex]

A. [tex]28x^3 - 62x^2 - 2x - 42[/tex]
B. [tex]28x^3 - 22x^2 - 2x - 42[/tex]
C. [tex]28x^3 - 22x^2 - 58x - 42[/tex]
D. [tex]28x^3 - 22x^2 - 2x + 42[/tex]

Sure! Let's multiply the polynomials [tex]$(7x^2 + 5x + 7)$[/tex] and [tex]$(4x - 6)$[/tex] step-by-step:

1. Distribute each term in the first polynomial to each term in the second polynomial:

- Multiply [tex]$7x^2$[/tex] by each term in the second polynomial:
- [tex]$7x^2 \times 4x = 28x^3$[/tex]
- [tex]$7x^2 \times -6 = -42x^2$[/tex]

- Multiply [tex]$5x$[/tex] by each term in the second polynomial:
- [tex]$5x \times 4x = 20x^2$[/tex]
- [tex]$5x \times -6 = -30x$[/tex]

- Multiply [tex]$7$[/tex] by each term in the second polynomial:
- [tex]$7 \times 4x = 28x$[/tex]
- [tex]$7 \times -6 = -42$[/tex]

2. Combine like terms:

- The [tex]$x^3$[/tex] term: [tex]$28x^3$[/tex]
- The [tex]$x^2$[/tex] terms: [tex]$-42x^2 + 20x^2 = -22x^2$[/tex]
- The [tex]$x$[/tex] terms: [tex]$-30x + 28x = -2x$[/tex]
- The constant term: [tex]$-42$[/tex]

3. Write the combined expression:

The result of multiplying the two polynomials is:

[tex]\[
28x^3 - 22x^2 - 2x - 42
\][/tex]

So, the correct answer is option B: [tex]$28x^3 - 22x^2 - 2x - 42$[/tex].