Answer :
To solve the problem of performing the indicated operations on the polynomials and writing the resulting polynomial in standard form, follow these steps:
1. Identify the given polynomials:
The first polynomial is [tex]\( 7x^7 + 5x^4 - 4 \)[/tex].
The second polynomial is [tex]\( 2x^7 + 9x^4 + 14 \)[/tex].
2. Set up the subtraction:
We need to subtract the second polynomial from the first polynomial:
[tex]\((7x^7 + 5x^4 - 4) - (2x^7 + 9x^4 + 14)\)[/tex].
3. Perform the subtraction for each term:
- Subtract the [tex]\(x^7\)[/tex] terms:
[tex]\(7x^7 - 2x^7 = 5x^7\)[/tex].
- Subtract the [tex]\(x^4\)[/tex] terms:
[tex]\(5x^4 - 9x^4 = -4x^4\)[/tex].
- Subtract the constant terms:
[tex]\(-4 - 14 = -18\)[/tex].
4. Write the resulting polynomial:
Combine all the terms obtained from the subtraction:
The resulting polynomial is [tex]\(5x^7 - 4x^4 - 18\)[/tex].
5. Write the polynomial in standard form:
A polynomial is in standard form when the terms are written in descending order of degrees. The polynomial [tex]\(5x^7 - 4x^4 - 18\)[/tex] is already in standard form because the terms are ordered from the highest degree (7) to the lowest (constant term).
Thus, the resulting polynomial is [tex]\(\mathbf{5x^7 - 4x^4 - 18}\)[/tex].
Therefore, the correct answer is b. [tex]\(5x^7 - 4x^4 - 18\)[/tex].
1. Identify the given polynomials:
The first polynomial is [tex]\( 7x^7 + 5x^4 - 4 \)[/tex].
The second polynomial is [tex]\( 2x^7 + 9x^4 + 14 \)[/tex].
2. Set up the subtraction:
We need to subtract the second polynomial from the first polynomial:
[tex]\((7x^7 + 5x^4 - 4) - (2x^7 + 9x^4 + 14)\)[/tex].
3. Perform the subtraction for each term:
- Subtract the [tex]\(x^7\)[/tex] terms:
[tex]\(7x^7 - 2x^7 = 5x^7\)[/tex].
- Subtract the [tex]\(x^4\)[/tex] terms:
[tex]\(5x^4 - 9x^4 = -4x^4\)[/tex].
- Subtract the constant terms:
[tex]\(-4 - 14 = -18\)[/tex].
4. Write the resulting polynomial:
Combine all the terms obtained from the subtraction:
The resulting polynomial is [tex]\(5x^7 - 4x^4 - 18\)[/tex].
5. Write the polynomial in standard form:
A polynomial is in standard form when the terms are written in descending order of degrees. The polynomial [tex]\(5x^7 - 4x^4 - 18\)[/tex] is already in standard form because the terms are ordered from the highest degree (7) to the lowest (constant term).
Thus, the resulting polynomial is [tex]\(\mathbf{5x^7 - 4x^4 - 18}\)[/tex].
Therefore, the correct answer is b. [tex]\(5x^7 - 4x^4 - 18\)[/tex].
