8. (a) Find specific numbers a, b, c, and d such that the polynomial f(x) = ax³ + bx² + cx + d has the values listed in the table below. Check, using f(5) = 165.
 

(b) Follow the instructions of the previous part for the table below. Check, using f(4) = 30.
 

9. (a) Show that

and that

(b) Let D be an n by n determinant, with the element a_ij in the ith row and jth column 0 if i > j. Show that D = a₁₁a₂₂a₃₃...a_nn.
 
 

Monday, July 6, 1998