Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Which polynomial represents the difference below?

\[ (3x^7 + 8x^4 + 7) - (x^4 - 2x) \]

A. \[ 3x^7 + 7x^4 + 2x + 7 \]
B. \[ 3x^7 + 9x^4 - 2x + 7 \]
C. \[ 3x^{11} + 7x^3 + 5x \]
D. \[ 2x^7 + 6x^3 + 6 \]

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].