If p(x)=2x^3+cx^2+16x+84 and x+2 is a factor of p(x),find the value of c.

c = -9

Step-by-step explanation:

Knowing that -2 is a root, you can do the synthetic division with an unknown value for c. Then solve for the value of c that makes the remainder be zero. See the attachment for the work.

The second attachment shows that (x+2) is a factor of the resulting cubic.

2nd one in the first row is correct