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 two polynomials:

[tex](3x^3 + 5x^2 - 2) + (4x^3 - 5x^2 - 2x + 6)[/tex]

A. [tex]7x^6 - 10x^4 - 2x - 12[/tex]
B. [tex]7x^3 - 2x - 8[/tex]
C. [tex]7x^3 - 2x + 4[/tex]

To add the two polynomials [tex]$(3x^3 + 5x^2 - 2) + (4x^3 - 5x^2 - 2x + 6)$[/tex], follow these steps:

1. Identify the Terms:
- The first polynomial, [tex]$3x^3 + 5x^2 - 2$[/tex], contains the terms:
- [tex]$3x^3$[/tex] (cubic term)
- [tex]$5x^2$[/tex] (quadratic term)
- [tex]$-2$[/tex] (constant term)

- The second polynomial, [tex]$4x^3 - 5x^2 - 2x + 6$[/tex], contains the terms:
- [tex]$4x^3$[/tex] (cubic term)
- [tex]$-5x^2$[/tex] (quadratic term)
- [tex]$-2x$[/tex] (linear term)
- [tex]$6$[/tex] (constant term)

2. Combine Like Terms:
- Cubic Terms: [tex]$3x^3 + 4x^3 = 7x^3$[/tex]
- Quadratic Terms: [tex]$5x^2 - 5x^2 = 0$[/tex] (these cancel each other out)
- Linear Terms: There is no [tex]$x$[/tex] term in the first polynomial, so just bring down [tex]$-2x$[/tex].
- Constant Terms: [tex]$-2 + 6 = 4$[/tex]

3. Form the Resultant Polynomial:
- Combine all the terms we found: [tex]$7x^3 + 0x^2 - 2x + 4$[/tex].

4. Simplify:
- Since the [tex]$x^2$[/tex] term is zero, we don't include it in our final expression.
- So, the resulting polynomial is [tex]$7x^3 - 2x + 4$[/tex].

Therefore, the resultant polynomial is [tex]$7x^3 - 2x + 4$[/tex], which corresponds to option (C).