To find the value of the expression [tex]\( w^2 + 3w - 11 \)[/tex] when [tex]\( w = -5 \)[/tex], we will substitute [tex]\(-5\)[/tex] for [tex]\( w \)[/tex] in the expression and simplify it step-by-step.
First, substitute [tex]\(-5\)[/tex] for [tex]\( w \)[/tex]:
[tex]\[
(-5)^2 + 3(-5) - 11
\][/tex]
Next, evaluate each part of the expression:
1. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
2. Calculate [tex]\(3 \cdot (-5)\)[/tex]:
[tex]\[
3 \cdot (-5) = -15
\][/tex]
3. Combine these values and then subtract 11:
[tex]\[
25 + (-15) - 11
\][/tex]
Simplify this step-by-step:
[tex]\[
25 - 15 = 10
\][/tex]
[tex]\[
10 - 11 = -1
\][/tex]
Therefore, the value of the expression when [tex]\( w = -5 \)[/tex] is:
[tex]\(
-1
\)[/tex]
The correct answer is D. -1.
