Answer
quotient$=x^2-\frac{2}{3}x-\frac{1}{9}$, remainder$=\frac{16}{9}x-\frac{17}{9}$
Work Step by Step
1. Use long division to get quotient$=x^2-\frac{2}{3}x-\frac{1}{9}$, remainder$=\frac{16}{9}x-\frac{17}{9}$
2. We have $(x^2-\frac{2}{3}x-\frac{1}{9})(3x^2+x+1)+(\frac{16}{9}x-\frac{17}{9})=3x^4-x^3+x-2$
