The polynomial P(x)=3x4+ax3+bx2+cx+d satisfies the following conditions:
• The remainder when P(x) is divided by (x−1) is −2.
• The remainder when P(x) is divided by (x+1) is 4.
• The remainder when P(x) is divided by (x−2) is 10.
• (x+3) is a factor of P(x).
(i) Translate each of the above statements into an equation involving a,b,c, and d.
(ii) Solve the resulting system of four simultaneous equations to determine the values of a,b,c, and d.