$Suppose we have some polynomial equation$ \; a_{n}x^n + a_{n-1}x^{n-1}+...+a_{0}=0 \; $given that each rational root is$\: x=\frac{a}{b}\:$with$\:gcd(a,b)=1\: ($meaning the greatest common divisor of$\: a \:$and$\:b \;$is$\: 1.)
$Substituting$\; x=\frac{a}{b}\; $into the equation you will see...