Answer :

To add the given polynomials [tex]\(x^3 - 2x^2 - 9\)[/tex] and [tex]\(5x^3 + 2x + 9\)[/tex], you should follow these steps:

1. Write Down Each Polynomial:
- The first polynomial is [tex]\(x^3 - 2x^2 - 9\)[/tex].
- The second polynomial is [tex]\(5x^3 + 2x + 9\)[/tex].

2. Align Terms by Degree:
- For [tex]\(x^3 - 2x^2 - 9\)[/tex]:
- [tex]\(x^3\)[/tex] term: [tex]\(x^3\)[/tex]
- [tex]\(x^2\)[/tex] term: [tex]\(-2x^2\)[/tex]
- [tex]\(x^1\)[/tex] term: [tex]\(0x\)[/tex] (It's not explicitly stated, but we understand that there's no [tex]\(x\)[/tex] term.)
- Constant term: [tex]\(-9\)[/tex]
- For [tex]\(5x^3 + 2x + 9\)[/tex]:
- [tex]\(x^3\)[/tex] term: [tex]\(5x^3\)[/tex]
- [tex]\(x^2\)[/tex] term: [tex]\(0x^2\)[/tex] (Again, not explicitly stated. There is no [tex]\(x^2\)[/tex] term.)
- [tex]\(x^1\)[/tex] term: [tex]\(2x\)[/tex]
- Constant term: [tex]\(9\)[/tex]

3. Add the Corresponding Coefficients:
- [tex]\(x^3\)[/tex] terms: [tex]\(1x^3 + 5x^3 = 6x^3\)[/tex]
- [tex]\(x^2\)[/tex] terms: [tex]\(-2x^2 + 0x^2 = -2x^2\)[/tex]
- [tex]\(x^1\)[/tex] terms: [tex]\(0x + 2x = 2x\)[/tex]
- Constant terms: [tex]\(-9 + 9 = 0\)[/tex]

4. Write the Resulting Polynomial:
Combine the results from step 3 to get the final sum of the polynomials:
- The resulting polynomial is [tex]\(6x^3 - 2x^2 + 2x + 0\)[/tex].

So, when you add the two polynomials, the result is [tex]\(6x^3 - 2x^2 + 2x\)[/tex].

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