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Answer :
To solve this problem, we need to add the two polynomials:
1. First, let's write down each polynomial:
- The first polynomial is [tex]\(8x^9 + 6x^6 - 2x + 6\)[/tex].
- The second polynomial is [tex]\(9x^9 + 4x^6 + 9x + 7\)[/tex].
2. Next, we add the coefficients of the terms with the same degree:
- For [tex]\(x^9\)[/tex], we have [tex]\(8 + 9 = 17\)[/tex].
- For [tex]\(x^6\)[/tex], we have [tex]\(6 + 4 = 10\)[/tex].
- For [tex]\(x\)[/tex], we have [tex]\(-2 + 9 = 7\)[/tex].
- For the constant term, we have [tex]\(6 + 7 = 13\)[/tex].
3. Combining these results, the sum of the polynomials is:
[tex]\[
17x^9 + 10x^6 + 7x + 13
\][/tex]
Let's check the options:
A. [tex]\(17x^9 + 10x^6 - 7x + 13\)[/tex]
B. [tex]\(17x^9 + 10x^6 + 7x + 13\)[/tex]
C. [tex]\(72x^9 + 24x^6 - 18x^2 + 13\)[/tex]
D. [tex]\(10x^9 + 17x^6 + 7x + 13\)[/tex]
The correct result is:
B. [tex]\(17x^9 + 10x^6 + 7x + 13\)[/tex]
1. First, let's write down each polynomial:
- The first polynomial is [tex]\(8x^9 + 6x^6 - 2x + 6\)[/tex].
- The second polynomial is [tex]\(9x^9 + 4x^6 + 9x + 7\)[/tex].
2. Next, we add the coefficients of the terms with the same degree:
- For [tex]\(x^9\)[/tex], we have [tex]\(8 + 9 = 17\)[/tex].
- For [tex]\(x^6\)[/tex], we have [tex]\(6 + 4 = 10\)[/tex].
- For [tex]\(x\)[/tex], we have [tex]\(-2 + 9 = 7\)[/tex].
- For the constant term, we have [tex]\(6 + 7 = 13\)[/tex].
3. Combining these results, the sum of the polynomials is:
[tex]\[
17x^9 + 10x^6 + 7x + 13
\][/tex]
Let's check the options:
A. [tex]\(17x^9 + 10x^6 - 7x + 13\)[/tex]
B. [tex]\(17x^9 + 10x^6 + 7x + 13\)[/tex]
C. [tex]\(72x^9 + 24x^6 - 18x^2 + 13\)[/tex]
D. [tex]\(10x^9 + 17x^6 + 7x + 13\)[/tex]
The correct result is:
B. [tex]\(17x^9 + 10x^6 + 7x + 13\)[/tex]
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