You could do synthetic division and put a k as the coefficient of x to arrive at
Since you know the remainder should be 0. Now you have:
Hi, I'm working with the factor theorem and need help with the following question:
If x^3 + 4x^2 + kx - 5 is divisible by (x+2), what is the value of k?
I thought of doing the following
f(-2)= (-2)^3 + 4(-2)^2 -2k - 5, and then replacing f(-2) with 0 since if f(x) is evenly divisible by d(x), then f(p) should equal 0, but obviously my thinking can't be correct since that would mean k = 0. I would be extremely grateful for any help. Thank you!