To evaluate the expression [tex]\(3(x-4) + 2x - x^2\)[/tex] for [tex]\(x = 5\)[/tex], we will perform step-by-step calculations. Let's break down and solve it step by step.
1. Begin by substituting [tex]\(x = 5\)[/tex] into the expression.
[tex]\[
3(5 - 4) + 2(5) - 5^2
\][/tex]
2. Simplify inside the parentheses.
[tex]\[
3(1) + 2(5) - 5^2
\][/tex]
3. Perform the multiplication.
[tex]\[
3 \cdot 1 + 2 \cdot 5 - 5^2
\][/tex]
[tex]\[
3 + 10 - 25
\][/tex]
4. Combine the results.
[tex]\[
3 + 10 = 13
\][/tex]
[tex]\[
13 - 25 = -12
\][/tex]
So, the final result of evaluating the expression [tex]\(3(x-4) + 2x - x^2\)[/tex] for [tex]\(x = 5\)[/tex] is [tex]\(-12\)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{-12}
\][/tex]
Answer: D. -12
