Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Add the polynomials below.

[tex]\left(x^5 + 2x^4 - 3x^2\right) + \left(7x^4 + x\right)[/tex]

A. [tex]x^5 + 9x^4 - 3x^2 + x[/tex]

B. [tex]5x^5 + 9x^4[/tex]

C. [tex]x^5 + 3x^3 + x[/tex]

D. [tex]8x^5 + 9x^4 - x[/tex]

To add the given polynomials [tex]$\left(x^5 + 2x^4 - 3x^2\right) + \left(7x^4 + x\right)$[/tex], follow these steps:

1. Write down the polynomials to be added:
[tex]\[
\left(x^5 + 2x^4 - 3x^2\right) \quad \text{and} \quad \left(7x^4 + x\right)
\][/tex]

2. Align terms with the same power:
[tex]\[
x^5 + 2x^4 - 3x^2 \quad \text{and} \quad 7x^4 + x
\][/tex]

3. Combined, the expressions become:
[tex]\[
x^5 + 2x^4 - 3x^2 \\
+ \quad \quad 7x^4 + x
\][/tex]

4. Group like terms together:
[tex]\[
(x^5) + (2x^4 + 7x^4) + (x) + (-3x^2)
\][/tex]

5. Simplify each grouped term:
[tex]\[
x^5 + (2+7)x^4 + x - 3x^2
\][/tex]

6. Perform the arithmetic:
[tex]\[
x^5 + 9x^4 + x - 3x^2
\][/tex]

So the sum of the polynomials is:
[tex]\[
x^5 + 9x^4 - 3x^2 + x
\][/tex]

Therefore, the correct answer is:

[tex]\[
\boxed{A. \, x^5 + 9x^4 - 3x^2 + x}
\][/tex]