Forrest,
Since the remainder on dividing f(x) by x^{2}  2 is bx we know that
f(x) = x^{5}  3x^{4}  6x^{3} + 3ax^{2}  24 = (x^{2}  2) g(x) + bx
for some polynomial g(x).
Since (x^{2}  2) is zero when x = √2 and when x = √2, substituting x = √2 and x = √2 in the equation above give two equations in the unknowns a and b. Solve for a and b.
Penny
