What is the product of the expression?

[tex]\left(7x^2\right)\left(2x^3+5\right)\left(x^2-4x-9\right)[/tex]

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

B. [tex]14x^6 - 56x^5 - 81x^4 - 140x^3 - 315x^2[/tex]

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

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

To find the product [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex], we'll follow these steps:

Step 1: Expand [tex]\((2x^3 + 5)(x^2 - 4x - 9)\)[/tex]

First, multiply each term in the first polynomial [tex]\((2x^3 + 5)\)[/tex] with each term in the second polynomial [tex]\((x^2 - 4x - 9)\)[/tex].

- Multiply [tex]\(2x^3\)[/tex] by each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- [tex]\(2x^3 \cdot x^2 = 2x^5\)[/tex]
- [tex]\(2x^3 \cdot (-4x) = -8x^4\)[/tex]
- [tex]\(2x^3 \cdot (-9) = -18x^3\)[/tex]

- Multiply [tex]\(5\)[/tex] by each term in [tex]\((x^2 - 4x - 9)\)[/tex]:
- [tex]\(5 \cdot x^2 = 5x^2\)[/tex]
- [tex]\(5 \cdot (-4x) = -20x\)[/tex]
- [tex]\(5 \cdot (-9) = -45\)[/tex]

Now combine all these results:
[tex]\[2x^5 - 8x^4 - 18x^3 + 5x^2 - 20x - 45\][/tex]

Step 2: Multiply the result by [tex]\(7x^2\)[/tex]

Now, multiply each term in the expanded polynomial by [tex]\(7x^2\)[/tex]:

- [tex]\(7x^2 \cdot 2x^5 = 14x^7\)[/tex]
- [tex]\(7x^2 \cdot (-8x^4) = -56x^6\)[/tex]
- [tex]\(7x^2 \cdot (-18x^3) = -126x^5\)[/tex]
- [tex]\(7x^2 \cdot 5x^2 = 35x^4\)[/tex]
- [tex]\(7x^2 \cdot (-20x) = -140x^3\)[/tex]
- [tex]\(7x^2 \cdot (-45) = -315x^2\)[/tex]

Now combine all these results to get the final expanded polynomial:
[tex]\[14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2\][/tex]

Therefore, the answer is:
[tex]\[14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2\][/tex]