To find the value of the expression [tex]\( w^2 + 3w - 11 \)[/tex] when [tex]\( w = -5 \)[/tex], we will substitute [tex]\(-5\)[/tex] into the expression for [tex]\( w \)[/tex] and simplify step-by-step.
1. Start with the expression:
[tex]\[ w^2 + 3w - 11 \][/tex]
2. Substitute [tex]\( w = -5 \)[/tex] into the expression:
[tex]\[ (-5)^2 + 3(-5) - 11 \][/tex]
3. Compute the square of [tex]\(-5\)[/tex]:
[tex]\[ 25 + 3(-5) - 11 \][/tex]
4. Multiply [tex]\( 3 \)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[ 25 - 15 - 11 \][/tex]
5. Simplify the expression step-by-step. First, add [tex]\( 25 \)[/tex] and [tex]\(-15\)[/tex]:
[tex]\[ 10 - 11 \][/tex]
6. Finally, subtract [tex]\( 11 \)[/tex] from [tex]\( 10 \)[/tex]:
[tex]\[ -1 \][/tex]
So, the value of the expression when [tex]\( w = -5 \)[/tex] is [tex]\(-1\)[/tex]. The correct answer is:
D. -1
