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------------------------------------------------ Simplify:

[tex]\left(x^4+4x+7\right)-\left(5x^4+7x-2\right)[/tex]

A. [tex]-4x^4 + 11x + 5[/tex]

B. [tex]6x^4 + 11x + 5[/tex]

C. [tex]-4x^4 - 3x + 9[/tex]

D. [tex]-4x^8 - 3x + 9[/tex]

Let's simplify the expression [tex]\((x^4 + 4x + 7) - (5x^4 + 7x - 2)\)[/tex] step-by-step.

1. Distribute the Negative Sign:

When you subtract a polynomial, you distribute the negative sign across each term in the second polynomial. The expression becomes:

[tex]\[
x^4 + 4x + 7 - 5x^4 - 7x + 2
\][/tex]

2. Combine Like Terms:

- For the [tex]\(x^4\)[/tex] terms:
[tex]\[
x^4 - 5x^4 = -4x^4
\][/tex]

- For the [tex]\(x\)[/tex] terms:
[tex]\[
4x - 7x = -3x
\][/tex]

- For the constant terms:
[tex]\[
7 + 2 = 9
\][/tex]

3. Simplified Expression:

Putting it all together, the simplified expression is:
[tex]\[
-4x^4 - 3x + 9
\][/tex]

So, the correct answer is option C: [tex]\(-4x^4 - 3x + 9\)[/tex].