(1) If f(x)= ax³–9x²+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 (x²–4x+3) is a factor of cx⁴+dx³–13x²–14x+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 2006-03-18 12:56:29