College

Choose the correct simplification of [tex]\left(5x^3 - 5x - 8\right) + \left(2x^3 + 4x + 2\right)[/tex].

A. [tex]7x^3 + x + 6[/tex]
B. [tex]3x^3 - 9x - 10[/tex]
C. [tex]3x^3 + 9x + 10[/tex]
D. [tex]7x^3 - x - 6[/tex]

Answer :

Sure! To simplify the expression [tex]\(\left(5x^3 - 5x - 8\right) + \left(2x^3 + 4x + 2\right)\)[/tex], follow these steps:

1. Combine the like terms for [tex]\(x^3\)[/tex]:
- [tex]\(5x^3\)[/tex] from the first polynomial
- [tex]\(2x^3\)[/tex] from the second polynomial

When you add these together:
[tex]\[
5x^3 + 2x^3 = 7x^3
\][/tex]

2. Combine the like terms for [tex]\(x\)[/tex]:
- [tex]\(-5x\)[/tex] from the first polynomial
- [tex]\(4x\)[/tex] from the second polynomial

When you add these together:
[tex]\[
-5x + 4x = -1x \quad \text{(or simply } -x\text{)}
\][/tex]

3. Combine the constant terms:
- [tex]\(-8\)[/tex] from the first polynomial
- [tex]\(2\)[/tex] from the second polynomial

When you add these together:
[tex]\[
-8 + 2 = -6
\][/tex]

Putting it all together, the simplified form of the expression [tex]\(\left(5x^3 - 5x - 8\right) + \left(2x^3 + 4x + 2\right)\)[/tex] is:

[tex]\[
7x^3 - x - 6
\][/tex]

So, the correct answer is:
[tex]\[
\boxed{7x^3 - x - 6}
\][/tex]