(1) If f(x)= ax
^{3}–9x
^{2}+bx+12 has x+1 and 2x–3 as factors, then find the values of a and b (without using the actual process of Division of Polynomials).
(2) If (x^{2}–4x+3) is a factor of cx^{4}+dx^{3}–13x^{2}–14x+24, then find the values of c and d (without using the actual process of Division of Polynomials).
(In reply to
Possible "how to" by e.g.)
Following your devlishly clever method, I deduce that a=2, b=1 and c=1, d=2.
It's a good thing that actual division was banned, as I doubt I ever
would have got the arithmetic right in doing actual division instead of
using your method (which may be viewed as exploiting the Remainder
Theorem).

Posted by Richard
on 20060318 12:56:29 