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Answer :
To find the polynomial that represents the difference between the two given polynomials, we'll follow these steps:
1. Identify Each Polynomial:
The first polynomial is [tex]\(3x^7 + 8x^4 + 7\)[/tex].
The second polynomial is [tex]\(x^4 - 2x\)[/tex].
2. Write the Expression for the Difference:
We'll be subtracting the second polynomial from the first:
[tex]\[
(3x^7 + 8x^4 + 7) - (x^4 - 2x)
\][/tex]
3. Distribute the Negative Sign:
When you subtract the second polynomial, distribute the negative sign across all the terms inside the parenthesis:
[tex]\[
3x^7 + 8x^4 + 7 - x^4 + 2x
\][/tex]
4. Combine Like Terms:
- The [tex]\(x^7\)[/tex] term: [tex]\(3x^7\)[/tex] (no [tex]\(x^7\)[/tex] in the second polynomial to combine).
- The [tex]\(x^4\)[/tex] terms: [tex]\(8x^4 - x^4 = 7x^4\)[/tex].
- The [tex]\(x\)[/tex] term: [tex]\(2x\)[/tex] (no [tex]\(x\)[/tex] in the first polynomial to combine).
- The constant term: [tex]\(7\)[/tex] (no constant in the second polynomial to combine).
5. Write the Resulting Polynomial:
After combining like terms, we have:
[tex]\[
3x^7 + 7x^4 + 2x + 7
\][/tex]
So, the polynomial that represents the difference is [tex]\(3x^7 + 7x^4 + 2x + 7\)[/tex].
The correct answer is option A: [tex]\(3x^7 + 7x^4 + 2x + 7\)[/tex].
1. Identify Each Polynomial:
The first polynomial is [tex]\(3x^7 + 8x^4 + 7\)[/tex].
The second polynomial is [tex]\(x^4 - 2x\)[/tex].
2. Write the Expression for the Difference:
We'll be subtracting the second polynomial from the first:
[tex]\[
(3x^7 + 8x^4 + 7) - (x^4 - 2x)
\][/tex]
3. Distribute the Negative Sign:
When you subtract the second polynomial, distribute the negative sign across all the terms inside the parenthesis:
[tex]\[
3x^7 + 8x^4 + 7 - x^4 + 2x
\][/tex]
4. Combine Like Terms:
- The [tex]\(x^7\)[/tex] term: [tex]\(3x^7\)[/tex] (no [tex]\(x^7\)[/tex] in the second polynomial to combine).
- The [tex]\(x^4\)[/tex] terms: [tex]\(8x^4 - x^4 = 7x^4\)[/tex].
- The [tex]\(x\)[/tex] term: [tex]\(2x\)[/tex] (no [tex]\(x\)[/tex] in the first polynomial to combine).
- The constant term: [tex]\(7\)[/tex] (no constant in the second polynomial to combine).
5. Write the Resulting Polynomial:
After combining like terms, we have:
[tex]\[
3x^7 + 7x^4 + 2x + 7
\][/tex]
So, the polynomial that represents the difference is [tex]\(3x^7 + 7x^4 + 2x + 7\)[/tex].
The correct answer is option A: [tex]\(3x^7 + 7x^4 + 2x + 7\)[/tex].
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