Answer
$f(x)=(x+i)(x+1)(2x+1)$
Work Step by Step
Step 1. Use the given coefficients of the polynomial to set up a division as shown in the figure.
Step 2. Perform a synthetic division and find the quotient as $2x^2+3x+1$.
Step 3. Factor $2x^2+3x+1$ to get $(x+1)(2x+1)$ thus $f(x)=(x+i)(x+1)(2x+1)$