Answer :
To find the polynomial that represents the difference given by [tex]\(8x^8 + 9x^6 - x + 7\)[/tex] and [tex]\(6x^8 + 4x^7 + 5\)[/tex], let's follow these steps:
1. Write down the polynomials:
- The first polynomial is [tex]\(8x^8 + 9x^6 - x + 7\)[/tex].
- The second polynomial is [tex]\(6x^8 + 4x^7 + 5\)[/tex].
2. Subtract the polynomials:
To find the difference, subtract each term of the second polynomial from the corresponding term in the first polynomial. If a term doesn't exist in one of the polynomials, assume its coefficient is 0.
- Subtract the [tex]\(x^8\)[/tex] terms: [tex]\(8x^8 - 6x^8 = 2x^8\)[/tex].
- Subtract the [tex]\(x^7\)[/tex] terms: Since the first polynomial has no [tex]\(x^7\)[/tex] term, consider it as [tex]\(0x^7\)[/tex], so [tex]\(0 - 4x^7 = -4x^7\)[/tex].
- Subtract the [tex]\(x^6\)[/tex] terms: [tex]\(9x^6 - 0x^6 = 9x^6\)[/tex].
- The first polynomial has an [tex]\(-x\)[/tex] term, and the second one has no [tex]\(x\)[/tex] term, so just keep [tex]\(-x\)[/tex].
- Subtract the constant terms: [tex]\(7 - 5 = 2\)[/tex].
3. Combine the results:
Putting it all together, the polynomial representing the difference is:
[tex]\[
2x^8 - 4x^7 + 9x^6 - x + 2
\][/tex]
Thus, the correct answer is D. [tex]\(2x^8 - 4x^7 + 9x^6 - x + 2\)[/tex].
1. Write down the polynomials:
- The first polynomial is [tex]\(8x^8 + 9x^6 - x + 7\)[/tex].
- The second polynomial is [tex]\(6x^8 + 4x^7 + 5\)[/tex].
2. Subtract the polynomials:
To find the difference, subtract each term of the second polynomial from the corresponding term in the first polynomial. If a term doesn't exist in one of the polynomials, assume its coefficient is 0.
- Subtract the [tex]\(x^8\)[/tex] terms: [tex]\(8x^8 - 6x^8 = 2x^8\)[/tex].
- Subtract the [tex]\(x^7\)[/tex] terms: Since the first polynomial has no [tex]\(x^7\)[/tex] term, consider it as [tex]\(0x^7\)[/tex], so [tex]\(0 - 4x^7 = -4x^7\)[/tex].
- Subtract the [tex]\(x^6\)[/tex] terms: [tex]\(9x^6 - 0x^6 = 9x^6\)[/tex].
- The first polynomial has an [tex]\(-x\)[/tex] term, and the second one has no [tex]\(x\)[/tex] term, so just keep [tex]\(-x\)[/tex].
- Subtract the constant terms: [tex]\(7 - 5 = 2\)[/tex].
3. Combine the results:
Putting it all together, the polynomial representing the difference is:
[tex]\[
2x^8 - 4x^7 + 9x^6 - x + 2
\][/tex]
Thus, the correct answer is D. [tex]\(2x^8 - 4x^7 + 9x^6 - x + 2\)[/tex].
