Answer :
We start with the expression
[tex]$$
3x^4 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x^4 + 7x^5 - 3x^3.
$$[/tex]
Step 1. Group like terms
Arrange the terms by their exponents:
- For [tex]\(x^5\)[/tex]: [tex]\(7x^5\)[/tex].
- For [tex]\(x^4\)[/tex]: [tex]\(3x^4 - 3x^4\)[/tex].
- For [tex]\(x^3\)[/tex]: [tex]\(2x^3 - 3x^3\)[/tex].
- For [tex]\(x^2\)[/tex]: [tex]\(-5x^2 + 4x^2\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(6x - 2x\)[/tex].
Step 2. Combine the grouped terms
1. [tex]\(x^5\)[/tex] term:
[tex]$$
7x^5.
$$[/tex]
2. [tex]\(x^4\)[/tex] terms:
[tex]$$
3x^4 - 3x^4 = 0.
$$[/tex]
3. [tex]\(x^3\)[/tex] terms:
[tex]$$
2x^3 - 3x^3 = -x^3.
$$[/tex]
4. [tex]\(x^2\)[/tex] terms:
[tex]$$
-5x^2 + 4x^2 = -x^2.
$$[/tex]
5. [tex]\(x\)[/tex] terms:
[tex]$$
6x - 2x = 4x.
$$[/tex]
Step 3. Write the simplified expression
Adding all the combined terms together we obtain
[tex]$$
7x^5 - x^3 - x^2 + 4x.
$$[/tex]
Thus, the expression simplifies to
[tex]$$
\boxed{7x^5 - x^3 - x^2 + 4x}.
$$[/tex]
This corresponds to option A.
[tex]$$
3x^4 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x^4 + 7x^5 - 3x^3.
$$[/tex]
Step 1. Group like terms
Arrange the terms by their exponents:
- For [tex]\(x^5\)[/tex]: [tex]\(7x^5\)[/tex].
- For [tex]\(x^4\)[/tex]: [tex]\(3x^4 - 3x^4\)[/tex].
- For [tex]\(x^3\)[/tex]: [tex]\(2x^3 - 3x^3\)[/tex].
- For [tex]\(x^2\)[/tex]: [tex]\(-5x^2 + 4x^2\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(6x - 2x\)[/tex].
Step 2. Combine the grouped terms
1. [tex]\(x^5\)[/tex] term:
[tex]$$
7x^5.
$$[/tex]
2. [tex]\(x^4\)[/tex] terms:
[tex]$$
3x^4 - 3x^4 = 0.
$$[/tex]
3. [tex]\(x^3\)[/tex] terms:
[tex]$$
2x^3 - 3x^3 = -x^3.
$$[/tex]
4. [tex]\(x^2\)[/tex] terms:
[tex]$$
-5x^2 + 4x^2 = -x^2.
$$[/tex]
5. [tex]\(x\)[/tex] terms:
[tex]$$
6x - 2x = 4x.
$$[/tex]
Step 3. Write the simplified expression
Adding all the combined terms together we obtain
[tex]$$
7x^5 - x^3 - x^2 + 4x.
$$[/tex]
Thus, the expression simplifies to
[tex]$$
\boxed{7x^5 - x^3 - x^2 + 4x}.
$$[/tex]
This corresponds to option A.
