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.
------------------------------------------------ What is the simplest form of [tex]\left(4x^3 + 6x - 7\right) + \left(3x^3 - 5x^2 - 5x\right)[/tex]?

A. [tex]7x^3 - 5x^2 - x - 7[/tex]
B. [tex]7x^3 - 5x^2 + x - 7[/tex]
C. [tex]7x^3 + x^2 - 5x - 7[/tex]
D. [tex]7x^6 - 4x^2 - 7[/tex]

To find the simplest form of the expression [tex]$(4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)$[/tex], we need to combine like terms. Let's go through the process step-by-step:

1. Identify the like terms:

- Terms with [tex]$x^3$[/tex]: [tex]$4x^3$[/tex] and [tex]$3x^3$[/tex]
- Terms with [tex]$x^2$[/tex]: There is no [tex]$x^2$[/tex] term in the first expression, and [tex]$-5x^2$[/tex] from the second expression.
- Terms with [tex]$x$[/tex]: [tex]$6x$[/tex] and [tex]$-5x$[/tex]
- Constant term: [tex]$-7$[/tex]

2. Combine the like terms:

- For [tex]$x^3$[/tex]:
- [tex]$4x^3 + 3x^3 = 7x^3$[/tex]

- For [tex]$x^2$[/tex]:
- Since there is no [tex]$x^2$[/tex] term in the first expression, we take [tex]$-5x^2$[/tex] from the second one, resulting in [tex]$-5x^2$[/tex].

- For [tex]$x$[/tex]:
- [tex]$6x - 5x = x$[/tex]

- For the constant term:
- [tex]$-7$[/tex] stays [tex]$-7$[/tex], as it's just a constant term.

3. Write the combined expression:

Putting it all together, the expression in its simplest form is:

[tex]\[
7x^3 - 5x^2 + x - 7
\][/tex]

So, the correct choice is [tex]$7x^3 - 5x^2 + x - 7$[/tex].