find T so x-3 is a factor of f(x)=x^3-4x^2+Tx+3

Answer 1

a little synthetic division reveals that

f(x) = (x-3)(x^2 - x + T-3)+ (3T-6)

If we want f(3) to be zero, then 3T-6=0, so T=2

f(x) = x^3 - 4x^2 + 2x + 3
= (x-3)(x^2 - x - 1)

Answer 2

or ...

if x-3 is a factor, then f(3) = 0
f(3) = 27 - 36 + 3T + 3 = 0
3T = 6
T = 2