What is the product?

[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]\(14x^6 - 56x^5 - 91x^4 - 140x^3 - 315x^2\)[/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 will expand the expression step-by-step to find the correct answer.

1. First, distribute [tex]\(7x^2\)[/tex] into the polynomial [tex]\(2x^3 + 5\)[/tex]:
[tex]\[
(7x^2)(2x^3 + 5) = (7x^2 \cdot 2x^3) + (7x^2 \cdot 5)
\][/tex]
[tex]\[
= 14x^5 + 35x^2
\][/tex]

2. Now take the result and multiply it with [tex]\(x^2 - 4x - 9\)[/tex]:
[tex]\[
(14x^5 + 35x^2)(x^2 - 4x - 9)
\][/tex]

3. Expand step-by-step by distributing each term of the first polynomial:

- Distribute [tex]\(14x^5\)[/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]

- Distribute [tex]\(35x^2\)[/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]

4. Combine all terms:

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

After performing these steps, we arrive at the expanded form:
[tex]\[ 14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2 \][/tex]

This is the fully expanded and simplified product of the given expression.