Let's simplify the given expression step-by-step:
Given expression:
[tex]\[
x^4 + 3x^3 - 2x^3 - 5x^2 - x + x^2 + x + 1 + 7x^4
\][/tex]
1. Combine like terms:
[tex]\[
x^4 + 7x^4
\][/tex]
This results in:
[tex]\[
8x^4
\][/tex]
Next, we look at the \(x^3\) terms:
[tex]\[
3x^3 - 2x^3
\][/tex]
This simplifies to:
[tex]\[
x^3
\][/tex]
Now we combine the \(x^2\) terms:
[tex]\[
-5x^2 + x^2
\][/tex]
This simplifies to:
[tex]\[
-4x^2
\][/tex]
Next, we combine the \(x\) terms:
[tex]\[
-x + x
\][/tex]
This results in:
[tex]\[
0x
\][/tex]
Finally, we have the constant term:
[tex]\[
+1
\][/tex]
2. Combine all simplified terms:
[tex]\[
8x^4 + x^3 - 4x^2 + 1
\][/tex]
From the provided multiple-choice options, this matches option C.
So, the simplified expression is:
[tex]\[
\boxed{8x^4 + x^3 - 4x^2 + 1}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\text{C. } 8x^4 + x^3 - 4x^2 + 1}
\][/tex]
