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

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

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

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

1. Distribute each term in the first polynomial by every term in the second polynomial:

- Multiply [tex]$7x^2$[/tex] by [tex]$4x$[/tex] to get [tex]$28x^3$[/tex].
- Multiply [tex]$7x^2$[/tex] by [tex]$-6$[/tex] to get [tex]$-42x^2$[/tex].

- Multiply [tex]$5x$[/tex] by [tex]$4x$[/tex] to get [tex]$20x^2$[/tex].
- Multiply [tex]$5x$[/tex] by [tex]$-6$[/tex] to get [tex]$-30x$[/tex].

- Multiply [tex]$7$[/tex] by [tex]$4x$[/tex] to get [tex]$28x$[/tex].
- Multiply [tex]$7$[/tex] by [tex]$-6$[/tex] to get [tex]$-42$[/tex].

2. Combine the results to form a new polynomial:

[tex]\[
28x^3 + (-42x^2) + 20x^2 + (-30x) + 28x + (-42)
\][/tex]

3. Combine like terms:

- Combine the [tex]$x^2$[/tex] terms: [tex]$-42x^2 + 20x^2 = -22x^2$[/tex].
- Combine the [tex]$x$[/tex] terms: [tex]$-30x + 28x = -2x$[/tex].

4. Final polynomial:

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

This matches answer choice B: [tex]$\boxed{28x^3 - 22x^2 - 2x - 42}$[/tex].