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
