Answer: The required remainder is 5.
Step-by-step explanation: We are given to find the remainder when we divide the following cubic polynomial by (x+2 :
3 f(x)=2x^ 3 +4x^ 2 - 6^ 2 -x+
(i)
We have the following theorem:
Remainder theorem: If a polynomial p(x) is divided by the factor (x-a), then the remainder is p(a).
So, for the given linear factor, we have
x + 2 = 0
Rightarrow x=-2
Substituting x = - 2 in equation (i), we get
f(- 2)
=2(-2)^ 3 +4(-2)^ 2 -(-2)+3
=-16+16+2+3
=5 .
Thus, the required remainder is 5.