Answer :
Alright, let's solve the problem step by step.
We're asked to subtract the second polynomial from the first polynomial:
First polynomial: [tex]\(-5x^4 + 2x^6 - 8 - 6x^5\)[/tex]
Second polynomial: [tex]\(5 + 2x^5 + 6x^6 + 9x^4\)[/tex]
To subtract these polynomials, we need to subtract each term of the second polynomial from the corresponding term in the first polynomial. If there is no corresponding term, simply treat it as subtracting zero. Let's go through the terms one by one:
1. [tex]\(x^6\)[/tex] terms:
[tex]\((2x^6) - (6x^6) = 2x^6 - 6x^6 = -4x^6\)[/tex]
2. [tex]\(x^5\)[/tex] terms:
[tex]\((-6x^5) - (2x^5) = -6x^5 - 2x^5 = -8x^5\)[/tex]
3. [tex]\(x^4\)[/tex] terms:
[tex]\((-5x^4) - (9x^4) = -5x^4 - 9x^4 = -14x^4\)[/tex]
4. Constant terms:
[tex]\((-8) - (5) = -8 - 5 = -13\)[/tex]
Now combine all these results to get the final polynomial:
[tex]\[
-4x^6 - 8x^5 - 14x^4 - 13
\][/tex]
So, the answer is: [tex]\(-4x^6 - 8x^5 - 14x^4 - 13\)[/tex].
This matches with the first option provided.
We're asked to subtract the second polynomial from the first polynomial:
First polynomial: [tex]\(-5x^4 + 2x^6 - 8 - 6x^5\)[/tex]
Second polynomial: [tex]\(5 + 2x^5 + 6x^6 + 9x^4\)[/tex]
To subtract these polynomials, we need to subtract each term of the second polynomial from the corresponding term in the first polynomial. If there is no corresponding term, simply treat it as subtracting zero. Let's go through the terms one by one:
1. [tex]\(x^6\)[/tex] terms:
[tex]\((2x^6) - (6x^6) = 2x^6 - 6x^6 = -4x^6\)[/tex]
2. [tex]\(x^5\)[/tex] terms:
[tex]\((-6x^5) - (2x^5) = -6x^5 - 2x^5 = -8x^5\)[/tex]
3. [tex]\(x^4\)[/tex] terms:
[tex]\((-5x^4) - (9x^4) = -5x^4 - 9x^4 = -14x^4\)[/tex]
4. Constant terms:
[tex]\((-8) - (5) = -8 - 5 = -13\)[/tex]
Now combine all these results to get the final polynomial:
[tex]\[
-4x^6 - 8x^5 - 14x^4 - 13
\][/tex]
So, the answer is: [tex]\(-4x^6 - 8x^5 - 14x^4 - 13\)[/tex].
This matches with the first option provided.
