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------------------------------------------------ What is the product?

\[ (7x^2)(2x^3+5)(x^2-4x-9) \]

A. \[ 14x^5-x^4-46x^3-58x^2-20x-45 \]

B. \[ 14x^6-56x^5-91x^4-140x^3-315x^2 \]

C. \[ 14x^7-56x^6-126x^5+35x^4-140x^3-315x^2 \]

D. \[ 14x^{12}-182x^6+35x^4-455x^2 \]

We want to find the product

[tex]$$
(7x^2)(2x^3+5)(x^2-4x-9).
$$[/tex]

Step 1. Multiply the first two factors:
Multiply [tex]$7x^2$[/tex] by each term in [tex]$2x^3+5$[/tex]:

[tex]\[
7x^2 \cdot 2x^3 = 14x^5, \quad 7x^2 \cdot 5 = 35x^2.
\][/tex]

So, the product of the first two factors is:

[tex]$$
14x^5 + 35x^2.
$$[/tex]

Step 2. Multiply the result by the third factor:
Now, multiply [tex]$(14x^5 + 35x^2)$[/tex] by [tex]$(x^2 - 4x - 9)$[/tex] by distributing each term:

1. Multiply [tex]$14x^5$[/tex] by each term in [tex]$(x^2-4x-9)$[/tex]:
[tex]\[
14x^5 \cdot x^2 = 14x^7,
\][/tex]
[tex]\[
14x^5 \cdot (-4x) = -56x^6,
\][/tex]
[tex]\[
14x^5 \cdot (-9) = -126x^5.
\][/tex]

2. Multiply [tex]$35x^2$[/tex] by each term in [tex]$(x^2-4x-9)$[/tex]:
[tex]\[
35x^2 \cdot x^2 = 35x^4,
\][/tex]
[tex]\[
35x^2 \cdot (-4x) = -140x^3,
\][/tex]
[tex]\[
35x^2 \cdot (-9) = -315x^2.
\][/tex]

Step 3. Combine the results:
Now, combine all the terms together:

[tex]$$
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2.
$$[/tex]

This is the product of the given factors.

Final Answer:
[tex]$$
\boxed{14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2}
$$[/tex]

This corresponds to the third option in the list provided.