<s>[INST] Find the equation from the given equation in which leading term has c0-efficient $1$ 
Find the  equation obtained from $5x^3-7x^2+8x-9=0$ into one in which the co-efficients of leading term is  unity and the others are integers.

Below I am showing my attempt:
Applying the transformation $x\mapsto x+h$,then $f(x)=5x^3-7x^2+8x-9$ transforms into $f(x+h)=5(x+h)^3-7(x+h)^2+8(x+h)-9$
$ =5(x^3+h^3+3x^2h+3xh^2)-7(x^2+h^2+2xh)+8(x+h)-9$.
But this is not giving anything feasible as the leading term of $x$ must have co-efficient $1$.
How can I arrive at it?Should I use any alternative transformation.
 [/INST] Then, divide it by $5$ to obtain: $$f’(x+h) = x^3+x^2(3h-\frac75) + x(3h^2-\frac{14h}{5}+\frac85) +(h^3-\frac{7h^2}{5}+\frac{8h}{5}-\frac95)$$
Now, note that $f’(x+h)$ is monic and the coefficients of every power of $x$ should $\in \mathbb{Z}$.
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