Answer
4, 2, or 0 positive real zeros.
2 or 0 negative real zeros.
Work Step by Step
Step 1. There are 4 sign changes in $f(x)$, based on the Descartes’ Rule of Signs, there may be 4, 2, or 0 positive real zeros.
Step 2. $f(-x)=12x^8+x^7+8x^4+2x^3-x+3$, there are 2 sign changes in $f(-x)$, based on the Descartes’ Rule of Signs, there may be 2 or 0 negative real zeros.