If p(x)=2x^3+cx^2-5x-6 and x+2 is a factor of p(x),find the value of c.

P(x) = 2x^3 + cx^2 - 5x - 6

Since (x + 2) is a factor,
p(-2) = 0 (1)
p(-2) = 2(-2)^3 + c(-2)^2 - 5(-2) - 6
p(-2) = -16 + 4c + 10 - 6
p(-2) = 4c - 12 (2)

Substitute (1) into (2)
4c - 12 = 0
4c = 12
c = 3

Therefore c = 3

Just in case you don't understand,
- I substituted (-2) because ((-2) + 2) = 0
- In order for something to be a factor, the whole of p(x) has to = 0 when you substitute in the new value of x

step-by-step explanation:

yes it is1. move over 2 points on the x-axis2. move over 2 points on the y-axis