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Answer :
To find the sum of the given polynomials, follow these steps:
1. Write down the polynomials:
[tex]\((7x^7 + 5x^5 - 3x + 7) + (3x^7 + 2x^5 + x + 2)\)[/tex].
2. Align the like terms:
Identify and group terms that have the same power of [tex]\(x\)[/tex].
- For [tex]\(x^7\)[/tex]: [tex]\(7x^7\)[/tex] and [tex]\(3x^7\)[/tex].
- For [tex]\(x^5\)[/tex]: [tex]\(5x^5\)[/tex] and [tex]\(2x^5\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(-3x\)[/tex] and [tex]\(x\)[/tex].
- Constant terms: [tex]\(7\)[/tex] and [tex]\(2\)[/tex].
3. Add the coefficients of the like terms:
- Add [tex]\(x^7\)[/tex] terms: [tex]\(7 + 3 = 10\)[/tex], so you have [tex]\(10x^7\)[/tex].
- Add [tex]\(x^5\)[/tex] terms: [tex]\(5 + 2 = 7\)[/tex], so you have [tex]\(7x^5\)[/tex].
- Add [tex]\(x\)[/tex] terms: [tex]\(-3 + 1 = -2\)[/tex], so you have [tex]\(-2x\)[/tex].
- Add constant terms: [tex]\(7 + 2 = 9\)[/tex].
4. Write down the resulting polynomial:
Combine all the results to form the sum of the polynomials:
[tex]\[
10x^7 + 7x^5 - 2x + 9
\][/tex]
Thus, the sum of the polynomials is [tex]\(10x^7 + 7x^5 - 2x + 9\)[/tex], which corresponds to option C.
1. Write down the polynomials:
[tex]\((7x^7 + 5x^5 - 3x + 7) + (3x^7 + 2x^5 + x + 2)\)[/tex].
2. Align the like terms:
Identify and group terms that have the same power of [tex]\(x\)[/tex].
- For [tex]\(x^7\)[/tex]: [tex]\(7x^7\)[/tex] and [tex]\(3x^7\)[/tex].
- For [tex]\(x^5\)[/tex]: [tex]\(5x^5\)[/tex] and [tex]\(2x^5\)[/tex].
- For [tex]\(x\)[/tex]: [tex]\(-3x\)[/tex] and [tex]\(x\)[/tex].
- Constant terms: [tex]\(7\)[/tex] and [tex]\(2\)[/tex].
3. Add the coefficients of the like terms:
- Add [tex]\(x^7\)[/tex] terms: [tex]\(7 + 3 = 10\)[/tex], so you have [tex]\(10x^7\)[/tex].
- Add [tex]\(x^5\)[/tex] terms: [tex]\(5 + 2 = 7\)[/tex], so you have [tex]\(7x^5\)[/tex].
- Add [tex]\(x\)[/tex] terms: [tex]\(-3 + 1 = -2\)[/tex], so you have [tex]\(-2x\)[/tex].
- Add constant terms: [tex]\(7 + 2 = 9\)[/tex].
4. Write down the resulting polynomial:
Combine all the results to form the sum of the polynomials:
[tex]\[
10x^7 + 7x^5 - 2x + 9
\][/tex]
Thus, the sum of the polynomials is [tex]\(10x^7 + 7x^5 - 2x + 9\)[/tex], which corresponds to option C.
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