Sure! Let's simplify the given expression step-by-step:
Given expression:
[tex]\[
(3x^2 + x + 5) - (4x^2 - 2x)
\][/tex]
1. Expand the expression by distributing the negative sign:
[tex]\[
3x^2 + x + 5 - 4x^2 + 2x
\][/tex]
2. Combine like terms:
Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
3x^2 - 4x^2 = -x^2
\][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[
x + 2x = 3x
\][/tex]
There is only one constant term:
[tex]\[
5
\][/tex]
3. Put all the combined terms together:
[tex]\[
-x^2 + 3x + 5
\][/tex]
So, the simplified form of the expression is:
[tex]\[
-x^2 + 3x + 5
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{-x^2 + 3x + 5}
\][/tex]
None of the given choices (A, B, C, D) match this simplified form. Based on the detailed, step-by-step solution, the simplified form is indeed [tex]\(-x^2 + 3x + 5\)[/tex]. Please recheck the provided choices.
