Answer: The required remainder is 5.
Step-by-step explanation: We are given to find the remainder of the following division :
\((2x^3-18x+5)\div (x-3).\)
We have the following theorem :
FACTOR THEOREM : If f(x) is a polynomial, then the remainder on dividing f(x) by (x - a) is f(a).
For the given division, we have
\(f(x)=2x^3-18x+5,\\\\(x-a)=(x-3)~~~~~\Rightarrow a=3.\)
Therefore, the remainder when f(x) is divided by (x - 3) is given by
\(f(3)=2\times3^3-18\times3+5=54-54+5=5.\)
Thus, the required remainder is 5.
