(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).

Can we use multiplication of the polynomials??? if so, here's my solution.
for prob. 1
take the other factor as (mx+n) multiply all the factors and solve the resultant equations after comparing the corresponding order. u will be with the possible answer as a = 2 and b = 1
similarly for prob.2 take the other factor as (lx^2+mx+n) and solve teh equations, u will get c = 1 and d = 2;

Posted by Ravi on 2006-03-20 06:38:58