Consider the polynomial
h(x)=x4+px3+qx2+rx+6.
It is known that h(1)=4, h(−1)=6, and that (x−2) is a factor of h(x).
(a) Set up the three equations in p, q, and r corresponding to the above conditions.
(b) Solve the system to obtain the numerical values of p, q, and r.
(c) Using the obtained coefficients, verify that (x−2) is a factor of h(x) by carrying out the division or otherwise.
Show all necessary steps.