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Answer :
To solve the subtraction of the given polynomials and write the result in standard form, follow these steps:
1. Write down the expressions:
- The first polynomial is [tex]\( 4x^8 - 5x^7 + 5x^6 + 7 \)[/tex].
- The second polynomial is [tex]\( 9x^8 - 2x^7 - 8x^6 + 8 \)[/tex].
2. Subtract the polynomials:
This involves subtracting each corresponding term in the second polynomial from the first polynomial. Be careful with the signs.
- The term for [tex]\(x^8\)[/tex] is: [tex]\(4x^8 - 9x^8 = -5x^8\)[/tex].
- The term for [tex]\(x^7\)[/tex] is: [tex]\(-5x^7 - (-2x^7) = -5x^7 + 2x^7 = -3x^7\)[/tex].
- The term for [tex]\(x^6\)[/tex] is: [tex]\(5x^6 - (-8x^6) = 5x^6 + 8x^6 = 13x^6\)[/tex].
- For the constant terms: [tex]\(7 - 8 = -1\)[/tex].
3. Put it all together:
Combine the results from the subtraction to get the final polynomial expression:
[tex]\[
-5x^8 - 3x^7 + 13x^6 - 1
\][/tex]
4. Write the polynomial in standard form:
A polynomial is in standard form when its terms are written in descending order of degrees. Thus:
[tex]\[
-5x^8 - 3x^7 + 13x^6 - 1
\][/tex]
Therefore, the result of the subtraction is [tex]\( -5x^8 - 3x^7 + 13x^6 - 1 \)[/tex], which corresponds to answer choice d.
1. Write down the expressions:
- The first polynomial is [tex]\( 4x^8 - 5x^7 + 5x^6 + 7 \)[/tex].
- The second polynomial is [tex]\( 9x^8 - 2x^7 - 8x^6 + 8 \)[/tex].
2. Subtract the polynomials:
This involves subtracting each corresponding term in the second polynomial from the first polynomial. Be careful with the signs.
- The term for [tex]\(x^8\)[/tex] is: [tex]\(4x^8 - 9x^8 = -5x^8\)[/tex].
- The term for [tex]\(x^7\)[/tex] is: [tex]\(-5x^7 - (-2x^7) = -5x^7 + 2x^7 = -3x^7\)[/tex].
- The term for [tex]\(x^6\)[/tex] is: [tex]\(5x^6 - (-8x^6) = 5x^6 + 8x^6 = 13x^6\)[/tex].
- For the constant terms: [tex]\(7 - 8 = -1\)[/tex].
3. Put it all together:
Combine the results from the subtraction to get the final polynomial expression:
[tex]\[
-5x^8 - 3x^7 + 13x^6 - 1
\][/tex]
4. Write the polynomial in standard form:
A polynomial is in standard form when its terms are written in descending order of degrees. Thus:
[tex]\[
-5x^8 - 3x^7 + 13x^6 - 1
\][/tex]
Therefore, the result of the subtraction is [tex]\( -5x^8 - 3x^7 + 13x^6 - 1 \)[/tex], which corresponds to answer choice d.
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