To simplify the expression [tex]\(2x^5 + 3x^3 - 5x^2 + x^2 + 7x + 1 + 7x^5 - 3x^3 - 4\)[/tex], we follow these steps:
1. Identify and Combine Like Terms:
- Terms with [tex]\(x^5\)[/tex]:
[tex]\[
2x^5 + 7x^5 = 9x^5
\][/tex]
- Terms with [tex]\(x^3\)[/tex]:
[tex]\[
3x^3 - 3x^3 = 0
\][/tex]
These terms cancel each other out.
- Terms with [tex]\(x^2\)[/tex]:
[tex]\[
-5x^2 + x^2 = -4x^2
\][/tex]
- Terms with [tex]\(x\)[/tex]:
[tex]\[
7x
\][/tex]
There are no other [tex]\(x\)[/tex] terms to combine with.
- Constant terms:
[tex]\[
1 - 4 = -3
\][/tex]
2. Combine all the simplified terms:
[tex]\[
9x^5 - 4x^2 + 7x - 3
\][/tex]
Hence, the simplified form of the given expression is:
[tex]\[
9x^5 - 4x^2 + 7x - 3
\][/tex]
Therefore, the correct answer is:
D. [tex]\(9x^5 - 4x^2 + 7x - 3\)[/tex]
