(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 (1), f(x) must be something like (x+1)(2x-3)g(x), so f(-1) and f(1.5) must be zero... setting x=-1 and x=1.5 will produce two equations with two unknowns (a and b) and that would be the solution.

In (2), the polynomial (let's call it p(x)) must be a multiple of (x2-4x+3), so p(1) and p(3) must be zero (since 1 and 3 are the roots of x2-4x+3); once again, we would get two equations with two unknowns (c and d).

As asked, no polynomials were divided for this solution.

Posted by e.g. on 2006-03-18 11:30:21