(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 (1), f(x) must be something like (x+1)(2x3)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 (x24x+3), so p(1) and p(3) must be zero (since 1 and 3 are the roots of x24x+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 20060318 11:30:21 