if(x)= ax 3 + 4 x 2+3x-4 and g(x)=x3-4x+a leave the same remainder when divided by (x-3).find the value of a
a little synthetic division reveals that
f(x)/(x-3) has remainder 41+27a
g(x)/(x-3) has remainder 15+a
41+27a = 15+a
26 + 26a = 0
a = -1
f(x) = -x^3 + 4x^2 + 3x - 4 = (x-3)(-x^2+x+6)+14
g(x) = x^3 - 4x - 1 = (x-3)(x^2+3x+5)+14