Explanation
The remainder theorem is stated as follows: 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).
Thus, to find the remainder when f(-2) divides
[tex]f(x)=-2x^3+x^2+4x-3[/tex]
we will simply substitute x =-2 into the function
[tex]f(-2)=-2(-2)^3+(-2)^2+4(-2)-3[/tex]
Simplifying further
[tex]f(-2)=-2\times-8+4-8-3=16+4-11=20-11=9[/tex]
Therefore, the answer is 9
