Let F(x)=x5+mx4+nx3+px2+qx+10.
The following information is given:
• x=1 is a zero of F(x).
• x=−2 is a zero of F(x).
• x=3 is a zero of F(x).
• When F(x) is divided by (x+1), the remainder is −12.
(i) Form the four equations involving m,n,p, and q that arise from the above conditions.
(ii) Solve the simultaneous equations obtained in part (i) to find the values of m,n,p, and q.