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Answer :
Let's simplify the expression step-by-step:
The original expression is:
[tex]\[ 3x^4 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x^4 + 7x^5 - 3x^3 \][/tex]
Step 1: Combine like terms.
1. [tex]\(x^5\)[/tex] terms:
- There is only one [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]\(2x^3 - 3x^3 = -1x^3\)[/tex]
4. [tex]\(x^2\)[/tex] terms:
- [tex]\(-5x^2 + 4x^2 = -1x^2\)[/tex]
5. [tex]\(x\)[/tex] terms:
- [tex]\(6x - 2x = 4x\)[/tex]
Step 2: Write down the simplified expression by combining all these results:
[tex]\[ 7x^5 + 0x^4 - 1x^3 - 1x^2 + 4x \][/tex]
Step 3: Remove zero coefficient terms for clarity:
[tex]\[ 7x^5 - x^3 - x^2 + 4x \][/tex]
So, the simplified expression is:
[tex]\[ 7x^5 - x^3 - x^2 + 4x \][/tex]
This corresponds to option D.
The original expression is:
[tex]\[ 3x^4 + 2x^3 - 5x^2 + 4x^2 + 6x - 2x - 3x^4 + 7x^5 - 3x^3 \][/tex]
Step 1: Combine like terms.
1. [tex]\(x^5\)[/tex] terms:
- There is only one [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]\(2x^3 - 3x^3 = -1x^3\)[/tex]
4. [tex]\(x^2\)[/tex] terms:
- [tex]\(-5x^2 + 4x^2 = -1x^2\)[/tex]
5. [tex]\(x\)[/tex] terms:
- [tex]\(6x - 2x = 4x\)[/tex]
Step 2: Write down the simplified expression by combining all these results:
[tex]\[ 7x^5 + 0x^4 - 1x^3 - 1x^2 + 4x \][/tex]
Step 3: Remove zero coefficient terms for clarity:
[tex]\[ 7x^5 - x^3 - x^2 + 4x \][/tex]
So, the simplified expression is:
[tex]\[ 7x^5 - x^3 - x^2 + 4x \][/tex]
This corresponds to option D.
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