To simplify the given expression:
[tex]\[ x^4 + 3x^3 - 2x^3 - 5x^2 - x + x^2 + x + 1 + 7x^4 \][/tex]
we begin by combining like terms. Let's break it down step-by-step:
1. Combine the [tex]\(x^4\)[/tex] terms:
[tex]\[
x^4 + 7x^4 = 8x^4
\][/tex]
2. Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
3x^3 - 2x^3 = x^3
\][/tex]
3. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-5x^2 + x^2 = -4x^2
\][/tex]
4. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
-x + x = 0x
\][/tex]
5. Combine the constant terms:
[tex]\[
1
\][/tex]
Putting it all together:
[tex]\[
8x^4 + x^3 - 4x^2 + 0x + 1
\][/tex]
Since [tex]\(0x\)[/tex] does not contribute to the final simplified expression, we can exclude it:
[tex]\[
8x^4 + x^3 - 4x^2 + 1
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[ \boxed{8x^4 + x^3 - 4x^2 + 1} \][/tex]
The correct answer from the provided choices is:
B. [tex]\(8x^4 + x^3 - 4x^2 + 1\)[/tex]
