As above, let $$f(x) = 3\cdot\frac{x^4+x^3+x^2+1}{x^2+x-2}.$$Give a polynomial $g(x)$ so that $f(x) + g(x)$ has a horizontal asymptote of $y=0$ as $x$ approaches positive infinity.
By long division, 3(x^4 + x^3 + x^2 + 1)/(x^2 + x - 2) = 3x^2 + 12 - 15/(x + 2) + 4/(x - 1), so g(x) = -3x^2 - 12.
I entered it but unfotuanetly it's incorrect.
Good, I hope it is.
Do not dump all your homework here and expect the rest of the world to do it for you.
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