If x+1 is a factor of the polynomial
Question:

If $x+1$ is a factor of the polynomial $2 x^{2}+k x$, then the value of $k$ is

(a) $-3$

(b) 4

(c) 2

(d)-2

Solution:

(c) Let p(x) = 2x2 + kx

Since, (x + 1) is a factor of p(x), then

p(-1)=0

2(-1)2 + k(-1) = 0

=> 2-k = 0 => k= 2

Hence, the value of k is 2.