Select the correct answer.

What is the simplified form of this expression?

[tex]\[ \left(-3x^2 + x + 5\right) - \left(4x^2 - 2x\right) \][/tex]

A. [tex]\(-x^2 + 3x - 11\)[/tex]

B. [tex]\(7x^2 + 3x - 5\)[/tex]

C. [tex]\(-7x^2 + 3x + 5\)[/tex]

D. None of the above



Answer :

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]