Answer
$-\frac{1}{2}$.
$f(x) =(2x+1)(x^2+1)$
Work Step by Step
Step 1. List possible rational real zeros $\frac{p}{q}: \pm1,\pm\frac{1}{2}$
Step 2. Use synthetic division to find one zero as shown in the figure to find a zero $x=-\frac{1}{2}$.
Step 3. Use the quotient to find other zeros: $2x^2+2=0$ no solution.
Step 4. Factor the polynomial $f(x)=(x+\frac{1}{2})(2x^2+2)=(2x+1)(x^2+1)$
