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Answer :
To simplify the expression [tex]\((4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x + 9)\)[/tex], you'll want to combine like terms. Here's how you can simplify it step by step:
1. Identify the like terms:
- [tex]\(x^3\)[/tex] terms: [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex]
- [tex]\(x^2\)[/tex] terms: There is one term, [tex]\(-5x^2\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(6x\)[/tex] and [tex]\(-5x\)[/tex]
- Constant terms: [tex]\(-7\)[/tex] and [tex]\(9\)[/tex]
2. Combine the coefficients of like terms:
- For [tex]\(x^3\)[/tex] terms: [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- For [tex]\(x^2\)[/tex] terms: Since there is no [tex]\(x^2\)[/tex] term in the first polynomial, it remains [tex]\(-5x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(6x - 5x = 1x\)[/tex] or simply [tex]\(x\)[/tex]
- For the constant terms: [tex]\(-7 + 9 = 2\)[/tex]
3. Write the simplified expression:
- Combine all the terms: [tex]\(7x^3 - 5x^2 + x + 2\)[/tex]
Therefore, the simplest form of the expression [tex]\((4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x + 9)\)[/tex] is:
[tex]\[ \boxed{7x^3 - 5x^2 + x + 2} \][/tex]
This corresponds to option A.
1. Identify the like terms:
- [tex]\(x^3\)[/tex] terms: [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex]
- [tex]\(x^2\)[/tex] terms: There is one term, [tex]\(-5x^2\)[/tex]
- [tex]\(x\)[/tex] terms: [tex]\(6x\)[/tex] and [tex]\(-5x\)[/tex]
- Constant terms: [tex]\(-7\)[/tex] and [tex]\(9\)[/tex]
2. Combine the coefficients of like terms:
- For [tex]\(x^3\)[/tex] terms: [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- For [tex]\(x^2\)[/tex] terms: Since there is no [tex]\(x^2\)[/tex] term in the first polynomial, it remains [tex]\(-5x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(6x - 5x = 1x\)[/tex] or simply [tex]\(x\)[/tex]
- For the constant terms: [tex]\(-7 + 9 = 2\)[/tex]
3. Write the simplified expression:
- Combine all the terms: [tex]\(7x^3 - 5x^2 + x + 2\)[/tex]
Therefore, the simplest form of the expression [tex]\((4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x + 9)\)[/tex] is:
[tex]\[ \boxed{7x^3 - 5x^2 + x + 2} \][/tex]
This corresponds to option A.
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