Find the remainder if we divide $(6{\mathrm{x}}^3 + {\mathrm{x}}^2- 2\mathrm{x} + 4)$ by $(\mathrm{x} - 2)$.

 

Let f(x) =  $6{\mathrm{x}}^3+{\mathrm{x}}^2-2\mathrm{x}+4$ divided by x - 2. 

i.e. x - 2 is a factor of the given polynomial.

Using the remainder theorem : 

f(2) = 6(2)³ +(2)² -2(2) + 4

       = 48 + 4 - 4 + 4 = 52