Given p(x) = x 4 + x 3 - 13x 2 - 25x - 12 what is the remainder when p(x) is divided by x - 4? describe the relationship between the linear expression and the polynomial?

I'm assuming the function is p(x) = x^4 + x^3 - 13x^2 - 25x - 12

If so, then we can plug in 4 to get

p(x) = x^4 + x^3 - 13x^2 - 25x - 12
p(4) = (4)^4 + (4)^3 - 13(4)^2 - 25(4) - 12
p(4) = 256 + 64 - 13(16) - 25(4) - 12
p(4) = 256 + 64 - 208 - 100 - 12
p(4) = 320 - 208 - 100 - 12
p(4) = 112 - 100 - 12
p(4) = 12 - 12
p(4) = 0

Since the result is 0, this means that x-4 is a factor of p(x). This is due to the remainder theorem.