To determine the value of [tex]\( k \)[/tex] such that [tex]\( (x+1) \)[/tex] is a factor of the polynomial [tex]\( 2x^2 + kx \)[/tex], we can use the fact that if [tex]\( (x+1) \)[/tex] is a factor, then the polynomial will be zero when [tex]\( x = -1 \)[/tex].
1. Given the polynomial:
[tex]\[
2x^2 + kx
\][/tex]
2. Substitute [tex]\( x = -1 \)[/tex] into the polynomial:
[tex]\[
2(-1)^2 + k(-1)
\][/tex]
3. Simplify the expression:
[tex]\[
2(1) + k(-1) = 2 - k
\][/tex]
4. Since [tex]\( (x+1) \)[/tex] is a factor, the polynomial should be zero when [tex]\( x = -1 \)[/tex]:
[tex]\[
2 - k = 0
\][/tex]
5. Solve for [tex]\( k \)[/tex]:
[tex]\[
k = 2
\][/tex]
Therefore, the value of [tex]\( k \)[/tex] is [tex]\(\boxed{2}\)[/tex].
So, the correct answer is:
c) 2
