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------------------------------------------------ Find the sum of the polynomials below:

[tex]\[
\left(8x^9 + 4x - 4\right) + \left(5x^9 + x + 5\right)
\][/tex]

A. [tex]$13x^9 + 5x + 1$[/tex]

B. [tex]$13x^9 - 5x + 1$[/tex]

C. [tex]$40x^{18} + 5x^2 + 1$[/tex]

D. [tex]$40x^9 + 4x^2 + 1$[/tex]

To find the sum of the two polynomials, we will add them term by term. Let's break it down:

The polynomials given are:
1. [tex]$8x^9 + 4x - 4$[/tex]
2. [tex]$5x^9 + x + 5$[/tex]

Step 1: Combine the [tex]$x^9$[/tex] terms

For the [tex]$x^9$[/tex] terms, we add the coefficients:
- The coefficient of [tex]$x^9$[/tex] in the first polynomial is 8.
- The coefficient of [tex]$x^9$[/tex] in the second polynomial is 5.

So, [tex]$8 + 5 = 13$[/tex]. This gives us a [tex]$13x^9$[/tex] term.

Step 2: Combine the [tex]$x$[/tex] terms

For the [tex]$x$[/tex] terms, we add the coefficients:
- The coefficient of [tex]$x$[/tex] in the first polynomial is 4.
- The coefficient of [tex]$x$[/tex] in the second polynomial is 1.

So, [tex]$4 + 1 = 5$[/tex]. This gives us a [tex]$5x$[/tex] term.

Step 3: Combine the constant terms

For the constant terms, we add them directly:
- The constant term in the first polynomial is -4.
- The constant term in the second polynomial is 5.

So, [tex]$-4 + 5 = 1$[/tex].

Putting it all together:

We've combined each corresponding term, which results in the polynomial:
[tex]\[13x^9 + 5x + 1\][/tex]

Therefore, the sum of the polynomials is:
[tex]\[ \boxed{13x^9 + 5x + 1} \][/tex]

This corresponds to option A.