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Answer :
Let's find the difference of the two polynomials step by step:
Given polynomials:
- Polynomial 1: [tex]\(7x^9 + 9x^5 + 15\)[/tex]
- Polynomial 2: [tex]\((10x^9 + 8x^5 + 12)\)[/tex]
To find the difference, we subtract the second polynomial from the first one:
[tex]\[
(7x^9 + 9x^5 + 15) - (10x^9 + 8x^5 + 12)
\][/tex]
Now, let's distribute the negative sign in front of the second polynomial:
[tex]\[
= 7x^9 + 9x^5 + 15 - 10x^9 - 8x^5 - 12
\][/tex]
Next, combine like terms:
- For the [tex]\(x^9\)[/tex] terms: [tex]\(7x^9 - 10x^9 = -3x^9\)[/tex]
- For the [tex]\(x^5\)[/tex] terms: [tex]\(9x^5 - 8x^5 = 1x^5\)[/tex] or simply [tex]\(x^5\)[/tex]
- Constant terms: [tex]\(15 - 12 = 3\)[/tex]
Putting it all together, the difference is:
[tex]\[
-3x^9 + x^5 + 3
\][/tex]
After analyzing the options provided:
- A. [tex]\(-3x^9 + x^6 + 3\)[/tex]
- B. [tex]\(17x^6 + x^8 + 27\)[/tex]
- C. [tex]\(-3x^9 + 17x^5 + 27\)[/tex]
- D. [tex]\(3x^9 + 17x^5 + 27\)[/tex]
We can see that our result matches none of the options exactly due to typing errors but matches most closely with:
A. [tex]\(-3x^9 + x^5 + 3\)[/tex]
So, the closest correct answer is option A.
Given polynomials:
- Polynomial 1: [tex]\(7x^9 + 9x^5 + 15\)[/tex]
- Polynomial 2: [tex]\((10x^9 + 8x^5 + 12)\)[/tex]
To find the difference, we subtract the second polynomial from the first one:
[tex]\[
(7x^9 + 9x^5 + 15) - (10x^9 + 8x^5 + 12)
\][/tex]
Now, let's distribute the negative sign in front of the second polynomial:
[tex]\[
= 7x^9 + 9x^5 + 15 - 10x^9 - 8x^5 - 12
\][/tex]
Next, combine like terms:
- For the [tex]\(x^9\)[/tex] terms: [tex]\(7x^9 - 10x^9 = -3x^9\)[/tex]
- For the [tex]\(x^5\)[/tex] terms: [tex]\(9x^5 - 8x^5 = 1x^5\)[/tex] or simply [tex]\(x^5\)[/tex]
- Constant terms: [tex]\(15 - 12 = 3\)[/tex]
Putting it all together, the difference is:
[tex]\[
-3x^9 + x^5 + 3
\][/tex]
After analyzing the options provided:
- A. [tex]\(-3x^9 + x^6 + 3\)[/tex]
- B. [tex]\(17x^6 + x^8 + 27\)[/tex]
- C. [tex]\(-3x^9 + 17x^5 + 27\)[/tex]
- D. [tex]\(3x^9 + 17x^5 + 27\)[/tex]
We can see that our result matches none of the options exactly due to typing errors but matches most closely with:
A. [tex]\(-3x^9 + x^5 + 3\)[/tex]
So, the closest correct answer is option A.
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