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 multiply these expressions step by step.

### Step 1: Multiply the First Two Expressions

First, let's multiply [tex]\(7x^2\)[/tex] by [tex]\(2x^3 + 5\)[/tex]. Use the distributive property:

[tex]\[
7x^2 \cdot (2x^3 + 5) = (7x^2 \cdot 2x^3) + (7x^2 \cdot 5)
\][/tex]

Calculating each term:
- [tex]\(7x^2 \cdot 2x^3 = 14x^{2+3} = 14x^5\)[/tex]
- [tex]\(7x^2 \cdot 5 = 35x^2\)[/tex]

So, the product of the first two expressions is:
[tex]\[
14x^5 + 35x^2
\][/tex]

### Step 2: Multiply the Result with the Third Expression

Now, multiply this result by the third expression [tex]\(x^2 - 4x - 9\)[/tex]:

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

Using the distributive property again, distribute each term in [tex]\(14x^5 + 35x^2\)[/tex] over [tex]\(x^2 - 4x - 9\)[/tex].

#### Distribute 14x^5:
- [tex]\(14x^5 \cdot x^2 = 14x^{5+2} = 14x^7\)[/tex]
- [tex]\(14x^5 \cdot (-4x) = -56x^{5+1} = -56x^6\)[/tex]
- [tex]\(14x^5 \cdot (-9) = -126x^5\)[/tex]

#### Distribute 35x^2:
- [tex]\(35x^2 \cdot x^2 = 35x^{2+2} = 35x^4\)[/tex]
- [tex]\(35x^2 \cdot (-4x) = -140x^{2+1} = -140x^3\)[/tex]
- [tex]\(35x^2 \cdot (-9) = -315x^2\)[/tex]

### Combine All Terms

Now, combine all the terms obtained:
[tex]\[
14x^7 - 56x^6 - 126x^5 + 35x^4 - 140x^3 - 315x^2
\][/tex]

So, the product of [tex]\(\left(7x^2\right)\left(2x^3+5\right)\left(x^2-4x-9\right)\)[/tex] is:

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