Use synthetic division to determine if the given value for $k$ is a zero of this polynomial. If not, determine $p(k)$. \[ p(x)=4 x^{4}-12 x^{3}-8 x^{2}+46 x-28 ; k=2 \] Answer Selecting an option will display any text boxes needed to complete your answer. Is k a zero of this polynomial? Yes O No

Step 1 ：Given the polynomial \(p(x) = 4x^4 - 12x^3 - 8x^2 + 46x - 28\) and \(k = 2\)

Step 2 ：To determine if \(k\) is a zero of the polynomial, we substitute \(k\) into the polynomial. If the result is zero, then \(k\) is a zero of the polynomial.

Step 3 ：Substituting \(k = 2\) into the polynomial, we get \(p(k) = 4(2)^4 - 12(2)^3 - 8(2)^2 + 46(2) - 28\)

Step 4 ：Solving the above expression, we find that \(p(k) = 0\)

Step 5 ：Since \(p(k) = 0\), we conclude that \(k = 2\) is a zero of the polynomial.

Step 6 ：\(\boxed{\text{Yes, k is a zero of this polynomial.}}\)