Answer :
To add the polynomials [tex]\((7x^6 + 10x^2 - 10)\)[/tex] and [tex]\((3x^6 - 6x^3 + 4)\)[/tex], follow these steps:
1. Identify like terms:
- The terms with [tex]\(x^6\)[/tex]: [tex]\(7x^6\)[/tex] and [tex]\(3x^6\)[/tex].
- The terms with [tex]\(x^3\)[/tex]: There is [tex]\(-6x^3\)[/tex] in the second polynomial, and no [tex]\(x^3\)[/tex] term in the first polynomial.
- The terms with [tex]\(x^2\)[/tex]: [tex]\(10x^2\)[/tex] from the first polynomial, and no [tex]\(x^2\)[/tex] term in the second polynomial.
- Constant terms: [tex]\(-10\)[/tex] and [tex]\(4\)[/tex].
2. Combine like terms:
- [tex]\(x^6\)[/tex] terms: [tex]\(7x^6 + 3x^6 = 10x^6\)[/tex]
- [tex]\(x^3\)[/tex] terms: Since the first polynomial doesn’t have an [tex]\(x^3\)[/tex] term, it remains [tex]\(-6x^3\)[/tex].
- [tex]\(x^2\)[/tex] terms: [tex]\(10x^2\)[/tex] (no like term in the second polynomial, so it stays the same).
- Constant terms: [tex]\(-10 + 4 = -6\)[/tex].
3. Write the resulting polynomial:
- Combine all the simplified terms to form the final polynomial:
[tex]\[
10x^6 - 6x^3 + 10x^2 - 6
\][/tex]
So, the result of adding the two polynomials is [tex]\(10x^6 - 6x^3 + 10x^2 - 6\)[/tex]. This corresponds to option: [tex]\(10x^6 - 6 x^3 + 10 x^2 - 6\)[/tex].
1. Identify like terms:
- The terms with [tex]\(x^6\)[/tex]: [tex]\(7x^6\)[/tex] and [tex]\(3x^6\)[/tex].
- The terms with [tex]\(x^3\)[/tex]: There is [tex]\(-6x^3\)[/tex] in the second polynomial, and no [tex]\(x^3\)[/tex] term in the first polynomial.
- The terms with [tex]\(x^2\)[/tex]: [tex]\(10x^2\)[/tex] from the first polynomial, and no [tex]\(x^2\)[/tex] term in the second polynomial.
- Constant terms: [tex]\(-10\)[/tex] and [tex]\(4\)[/tex].
2. Combine like terms:
- [tex]\(x^6\)[/tex] terms: [tex]\(7x^6 + 3x^6 = 10x^6\)[/tex]
- [tex]\(x^3\)[/tex] terms: Since the first polynomial doesn’t have an [tex]\(x^3\)[/tex] term, it remains [tex]\(-6x^3\)[/tex].
- [tex]\(x^2\)[/tex] terms: [tex]\(10x^2\)[/tex] (no like term in the second polynomial, so it stays the same).
- Constant terms: [tex]\(-10 + 4 = -6\)[/tex].
3. Write the resulting polynomial:
- Combine all the simplified terms to form the final polynomial:
[tex]\[
10x^6 - 6x^3 + 10x^2 - 6
\][/tex]
So, the result of adding the two polynomials is [tex]\(10x^6 - 6x^3 + 10x^2 - 6\)[/tex]. This corresponds to option: [tex]\(10x^6 - 6 x^3 + 10 x^2 - 6\)[/tex].
