$f(x)=5 x^{4}-12 x^{2}+2 x+k$ is divided by $x-2$, th remainder is 28 , then $k=$ A) -8 B) -36 C) -16 D) 8 E) 16

Step 1 ：According to the Remainder Theorem, if a polynomial f(x) is divided by x - c, then the remainder is f(c). In this case, we are given that the remainder is 28 when f(x) is divided by x - 2. Therefore, we can set up the equation f(2) = 28 and solve for k.

Step 2 ：\(f(x) = 5x^4 - 12x^2 + 2x + k\)

Step 3 ：\(f(2) = 5(2)^4 - 12(2)^2 + 2(2) + k = 28\)

Step 4 ：\(k + 36 = 28\)

Step 5 ：\(k = -8\)

Step 6 ：\(\boxed{-8}\)