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------------------------------------------------ Which polynomial represents the difference below?

[tex]x^7 - 3x + 10 - \left(9x^8 + 4x\right)[/tex]

A. [tex]-9x^8 + x^7 + x + 10[/tex]
B. [tex]-9x^{15} + 12x + 10[/tex]
C. [tex]-9x^8 + x^7 - 7x + 10[/tex]
D. [tex]-9x^{15} + x^7 + x + 10[/tex]

To solve for the polynomial representing the difference, we need to subtract the polynomials given in the problem:

The initial expression is:
[tex]\[ x^7 - 3x + 10 - (9x^8 + 4x) \][/tex]

To subtract these, we'll distribute the negative sign in front of the second polynomial across its terms:
[tex]\[ = x^7 - 3x + 10 - 9x^8 - 4x \][/tex]

Next, rearrange the terms to combine like terms:
[tex]\[ = -9x^8 + x^7 - 3x - 4x + 10 \][/tex]

Now, combine the like terms ([tex]\(-3x\)[/tex] and [tex]\(-4x\)[/tex]):
[tex]\[ = -9x^8 + x^7 - 7x + 10 \][/tex]

Therefore, the polynomial that represents the difference is:
[tex]\[ -9x^8 + x^7 - 7x + 10 \][/tex]

So, the correct answer is:
C. [tex]\(-9x^8 + x^7 - 7x + 10\)[/tex]