Answer
$(x^4-x^2+1)(x^2-x+1)(x^2+x+1)$
Work Step by Step
Step 1. Let $y=x^2$, we have $x^8+x^4+1=y^4+y^2+1$
Step 2. Use the formula obtained from the previous exercise, we have $y^4+y^2+1=(y^2-y+1)(y^2+y+1)$
Step 3. Replace $y$ with $x^2$, we have $x^8+x^4+1=(x^4-x^2+1)(x^4+x^2+1)$
Step 4. Use the formula obtained from the previous exercise for the second term, we have $x^4+x^2+1=(x^2-x+1)(x^2+x+1)$
Step 5. Thus $x^8+x^4+1=(x^4-x^2+1)(x^2-x+1)(x^2+x+1)$
