<s>[INST] How to write the following polynomial in $(1-\frac{x}{a}) (1-\frac{x}{b}) (1-\frac{x}{c}) (1-\frac{x}{d})$? I was given the following problem:
Write the polynomial $f(x) = \frac{1}{24} \displaystyle \prod_{i \mathop = 1}^4 (x-i)$ in the form $(1-\frac{x}{a}) (1-\frac{x}{b}) (1-\frac{x}{c}) (1-\frac{x}{d})$
So far I have done this:
$f(x) = \frac{1}{24} \displaystyle \prod_{i \mathop = 1}^4 (x-i) = \frac{1}{24}(x-1)(x-2)(x-3)(x-4) 
= \frac{1}{24}(1-x)(2-x)(3-x)(4-x)
= (\frac{1-x}{1}) (\frac{2-x}{2}) (\frac{3-x}{3}) (\frac{4-x}{4})
= ({1-x}) (1-\frac{x}{2}) (1-\frac{x}{3}) (1-\frac{x}{4})$
EDIT: Seems like I got it, thanks for all the help!
 [/INST] hint:roots of the polynomial have to be same , what are the roots of l.h.s and r.h.s and then compare
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