Mathematics Asked by thinkingeye on January 18, 2021
I have a simple question.
I have a polynomial defined by
$$
left(r-xright)^n = a_0 + a_1 x + … + a_n x^n
$$
Is there a simple expression if I put the coefficients in reverse order?
$$
a_n + a_{n-1} x + … + a_1 x^{n-1} a_0 x^n = ?
$$
If $r = 1$ it is easy but for other $r$ I don’t know how to do it.
Edit solution:
Thanks to the general answer of paul blart math cop, the simple expression with reversed coefficient order is:
$$
x^n left(r-frac{1}{x}right)^n = left(rx-1right)^n
$$
Letting $f(x)$ be a polynomial of degree $n$, the polynomial with reversed coefficients to $f$ is $x^n f(1/x)$.
Correct answer by paul blart math cop on January 18, 2021
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