Solution
The remainder theorems state that when a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k).
Given
[tex]f(x)=4x^3-10x^2+10x-4[/tex]
since f(x) is divided by x - 2, the remainder is
[tex]f(2)=4(2)^3-10(2)^2+10(2)-4=4(8)-10(4)+20-4=32-40+20-4=8[/tex]
Therefore, the remainder is 8
