To determine which option the expression [tex]\(\left(5 x^2 - x + 4\right) - 3\left(x^2 - x - 2\right)\)[/tex] is equivalent to, we need to simplify it step-by-step.
Let's begin by expanding and simplifying the given expression:
1. Distribute the terms within each bracket:
[tex]\[
\left(5 x^2 - x + 4\right) - 3\left(x^2 - x - 2\right)
\][/tex]
First, expand the second part of the expression by distributing the -3 to each term inside the parentheses:
[tex]\[
-3(x^2 - x - 2) = -3 \cdot x^2 + 3 \cdot x + 3 \cdot 2 = -3x^2 + 3x + 6
\][/tex]
2. Rewrite the expression with this expansion:
[tex]\[
\left(5 x^2 - x + 4\right) - 3x^2 + 3x + 6
\][/tex]
3. Combine like terms:
Let's group together the [tex]\(x^2\)[/tex] terms, the [tex]\(x\)[/tex] terms, and the constant terms:
[tex]\[
5x^2 - 3x^2 = 2x^2
\][/tex]
[tex]\[
-x + 3x = 2x
\][/tex]
[tex]\[
4 + 6 = 10
\][/tex]
4. Combine the simplified terms:
[tex]\[
2x^2 + 2x + 10
\][/tex]
This final expression is [tex]\(2x^2 + 2x + 10\)[/tex].
Therefore, the correct option is:
(2) [tex]\(2 x^2 + 2 x + 10\)[/tex]
