Question

The value of p for which the polynomial 2x4+3x3+2px2+3x+6 is exactly divisible by (x+2)is

Answer 1

If a polynomial is exactly divisible by a binomial $x-a$, then $a$ is its root.

$a=-2\\2\cdot(-2)^4+3\cdot(-2)^3+2p\cdot (-2)^2+3\cdot(-2)+6=0\\32-24+8p-6+6=0\\8p=-8\\\boxed{p=-1}$