Answer
false
Work Step by Step
The Rational Zero Theorem$:$
If $f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}$
has INTEGER coefficients and
$\displaystyle \frac{p}{q}$ (where $p$ is reduced to lowest terms)
is a rational zero of $f$,
then $p$ is a factor of the constant term, $a_{0}$, and
$q$ is a factor of the leading coefficient, $a_{n}$.
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$p=$1 is a factor of 1 ($a_{o}$, constant$),$
$q=2$ is NOT a factor of 3 ($a_{4}$, leading)
$\displaystyle \frac{1}{2}$ is NOT a zero (no need to test)
