What is the product of the following expression?

[tex](7x^2)(2x^3 + 5)(x^2 - 4x - 9)[/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 of the given expression, we will multiply the three polynomials step-by-step:

Expression to simplify:
[tex]\[
7x^2 \cdot \left(2x^3 + 5\right) \cdot \left(x^2 - 4x - 9\right)
\][/tex]

### Step 1: Multiply the first two terms:
- Start with [tex]$ 7x^2 $[/tex] and [tex]$ (2x^3 + 5) $[/tex].

[tex]\[
7x^2 \cdot (2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5
\][/tex]
- Multiply each term:

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

- Combined, the result is:

[tex]\[
14x^5 + 35x^2
\][/tex]

### Step 2: Multiply the result with the third term:
- Now multiply [tex]$ (14x^5 + 35x^2) $[/tex] with [tex]$ (x^2 - 4x - 9) $[/tex].

[tex]\[
(14x^5 + 35x^2) \cdot (x^2 - 4x - 9)
\][/tex]

- Distribute each term:

[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]
[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 all the terms:
- Arrange and combine like terms:

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

This is the simplified expression for the given polynomials’ product.