Select the correct answer.

What is the simplified form of this expression?

[tex]\[
\left(-x^2 + x\right) + \left(4x^2 - x - 1\right)
\][/tex]

A. [tex]\(3x^2 - 1\)[/tex]
B. [tex]\(-5x^2 + 2x + 1\)[/tex]
C. [tex]\(-3x^2 + 1\)[/tex]
D. [tex]\(5x^2 + 2x - 1\)[/tex]



Answer :

To simplify the given expression [tex]\(\left(-x^2 + x\right) + \left(4x^2 - x - 1\right)\)[/tex], follow these steps:

1. Distribute any signs (if necessary):
In this case, everything is already distributed, so we can move to combining like terms directly.

2. Combine like terms:

- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ -x^2 + 4x^2 = 3x^2 \][/tex]

- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ x - x = 0 \][/tex]

- Combine the constant terms:
[tex]\[ -1 \][/tex]

3. Write down the simplified expression:
[tex]\[ 3x^2 - 1 \][/tex]

Thus, the simplified form of the expression [tex]\(\left(-x^2 + x\right) + \left(4x^2 - x - 1\right)\)[/tex] is:
[tex]\[ 3x^2 - 1 \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{3x^2 - 1} \][/tex]

So, the correct option is:
[tex]\[ \text{A. } 3x^2 - 1 \][/tex]