To simplify the given expression [tex]\(\left(-x^2 + x\right) + \left(4x^2 - x - 1\right)\)[/tex], we need to follow these steps:
1. Combine like terms by grouping the [tex]\(x^2\)[/tex] terms, the [tex]\(x\)[/tex] terms, and the constant terms separately.
The given expression is:
[tex]\[
\left(-x^2 + x\right) + \left(4x^2 - x - 1\right)
\][/tex]
2. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-x^2 + 4x^2 = 3x^2
\][/tex]
3. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
x - x = 0
\][/tex]
4. Combine the constant terms:
[tex]\[
-1
\][/tex]
5. Putting it all together, we get:
[tex]\[
3x^2 + 0x - 1
\][/tex]
Simplifying the term [tex]\(0x\)[/tex], the expression becomes:
[tex]\[
3x^2 - 1
\][/tex]
So, the simplified form of the expression is:
[tex]\[
3x^2 - 1
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{3x^2 - 1}
\][/tex]
Thus, the correct choice is:
[tex]\[
\text{B. } 3x^2 - 1
\][/tex]
