Solution
We have the polynomial
[tex]f(x)=-2x^3+x^2+4x-3[/tex]
Usin the remainder theorem, we find f(-2) by substituting x = -2
So we have
[tex]\begin{gathered} f(x)=-2x^{3}+x^{2}+4x-3 \\ \\ f(-2)=-2(-2)^3+(-2)^2+4(-2)-3 \\ \\ f(-2)=-2(-8)+4-8-3 \\ \\ f(-2)=16+4-8-3 \\ \\ f(-2)=20-11 \\ \\ f(-2)=9 \end{gathered}[/tex]
Therefore, the remainder is
[tex]9[/tex]
