Answer :
To add the polynomials [tex]\((-8x^4 - 7x^3 + 7x)\)[/tex] and [tex]\((-7x^4 + 9x^3 - 9)\)[/tex], we'll follow these steps:
1. Align the Polynomials by Like Terms:
Write each polynomial so that like terms are aligned. This helps ensure we add the correct terms together.
- Polynomial 1: [tex]\(-8x^4 - 7x^3 + 0x^2 + 7x + 0\)[/tex]
- Polynomial 2: [tex]\(-7x^4 + 9x^3 + 0x^2 + 0x - 9\)[/tex]
2. Add the Coefficients of Like Terms:
Combine the coefficients of matching powers of [tex]\(x\)[/tex].
- For [tex]\(x^4\)[/tex]:
[tex]\((-8) + (-7) = -15\)[/tex]
- For [tex]\(x^3\)[/tex]:
[tex]\((-7) + 9 = 2\)[/tex]
- For [tex]\(x^2\)[/tex]:
[tex]\(0 + 0 = 0\)[/tex]
- For [tex]\(x^1\)[/tex]:
[tex]\(7 + 0 = 7\)[/tex]
- Constant term:
[tex]\(0 + (-9) = -9\)[/tex]
3. Write the Resulting Polynomial:
Combine all the results to get the final polynomial:
[tex]\(-15x^4 + 2x^3 + 0x^2 + 7x - 9\)[/tex]
So, the result of adding the two polynomials is:
[tex]\(-15x^4 + 2x^3 + 7x - 9\)[/tex]
1. Align the Polynomials by Like Terms:
Write each polynomial so that like terms are aligned. This helps ensure we add the correct terms together.
- Polynomial 1: [tex]\(-8x^4 - 7x^3 + 0x^2 + 7x + 0\)[/tex]
- Polynomial 2: [tex]\(-7x^4 + 9x^3 + 0x^2 + 0x - 9\)[/tex]
2. Add the Coefficients of Like Terms:
Combine the coefficients of matching powers of [tex]\(x\)[/tex].
- For [tex]\(x^4\)[/tex]:
[tex]\((-8) + (-7) = -15\)[/tex]
- For [tex]\(x^3\)[/tex]:
[tex]\((-7) + 9 = 2\)[/tex]
- For [tex]\(x^2\)[/tex]:
[tex]\(0 + 0 = 0\)[/tex]
- For [tex]\(x^1\)[/tex]:
[tex]\(7 + 0 = 7\)[/tex]
- Constant term:
[tex]\(0 + (-9) = -9\)[/tex]
3. Write the Resulting Polynomial:
Combine all the results to get the final polynomial:
[tex]\(-15x^4 + 2x^3 + 0x^2 + 7x - 9\)[/tex]
So, the result of adding the two polynomials is:
[tex]\(-15x^4 + 2x^3 + 7x - 9\)[/tex]
