Let's simplify the given algebraic expression step by step:
Given:
[tex]\[ \left(-3x^2 + x + 5\right) - \left(4x^2 - 2x\right) \][/tex]
1. Distribute the negative sign through the second set of parentheses:
[tex]\[ -3x^2 + x + 5 - 4x^2 + 2x \][/tex]
2. Combine like terms by grouping similar terms together:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(-3x^2\)[/tex] and [tex]\(-4x^2\)[/tex]:
[tex]\[ -3x^2 - 4x^2 = -7x^2 \][/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(x\)[/tex] and [tex]\(2x\)[/tex]:
[tex]\[ x + 2x = 3x \][/tex]
- The constant term remains [tex]\(+5\)[/tex].
So, the simplified expression is:
[tex]\[ -7x^2 + 3x + 5 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{C.\ -7x^2 + 3x + 5} \][/tex]
