What is the product?

[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]

Sure! Let's break down the problem step by step to find the product of the given expression:

We want to find the product:
[tex]\[
(7x^2) \cdot (2x^3 + 5) \cdot (x^2 - 4x - 9)
\][/tex]

Step 1: Distribute [tex]\(7x^2\)[/tex] into the first parentheses [tex]\((2x^3 + 5)\)[/tex]:
[tex]\[
7x^2 \cdot (2x^3 + 5) = 7x^2 \cdot 2x^3 + 7x^2 \cdot 5
\][/tex]
[tex]\[
= 14x^5 + 35x^2
\][/tex]

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

Step 2: Distribute each term in [tex]\((14x^5 + 35x^2)\)[/tex] into [tex]\((x^2 - 4x - 9)\)[/tex]:

First, distribute [tex]\(14x^5\)[/tex]:
[tex]\[
14x^5 \cdot (x^2 - 4x - 9) = 14x^5 \cdot x^2 + 14x^5 \cdot (-4x) + 14x^5 \cdot (-9)
\][/tex]
[tex]\[
= 14x^7 - 56x^6 - 126x^5
\][/tex]

Next, distribute [tex]\(35x^2\)[/tex]:
[tex]\[
35x^2 \cdot (x^2 - 4x - 9) = 35x^2 \cdot x^2 + 35x^2 \cdot (-4x) + 35x^2 \cdot (-9)
\][/tex]
[tex]\[
= 35x^4 - 140x^3 - 315x^2
\][/tex]

Step 3: Combine all the terms we obtained from distributing:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]

Therefore, the product of [tex]\((7x^2)(2x^3 + 5)(x^2 - 4x - 9)\)[/tex] is:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]

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