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Given data:
The given equation is x^3-3x^2-37.
The given expression can be written as,
[tex]\begin{gathered} x^3-3x^2-37=x^2(x-5)+2x(x-5)+10(x-5)+13 \\ x^3-3x^2-37=(x-5)(x^2+2x+10)+13 \end{gathered}[/tex]Thus, when x^3-3x^2-37 is divide by (x-5) we get 13 as a remainder, so the correct option is (E).