Question

For what value of k is the polynomial 2x²+3x³+2xk²+3x+6 exactly divisible by (x+2). Show that (x+3) is a factor of x³+x²-4x+6

Answer 1

There is a slight mistake in your question. Actually it must have been

2x^4+3x³+2xk²+3x+6=0(depending on the order in which you have written the coefficients)

(x+2)=0
x=-2

Substitute x=-2
2*16-3*8-2k²*2+3*-2+6=0
32-24-2k²-6+6=0
8=2k²
k²=4
k=+/-2