Find the remainder when $x^4 +x + 2$ is divided by $x-3$.
To find the remainder when a polynomial is divided by a linear factor, I can use the remainder theorem, which says that the remainder is equal to the value of the polynomial when I plug in the root of the divisor. The root of $x-3$ is $x=3$, so I need to evaluate $x^4 +x + 2$ at $x=3$. That means I need to replace every $x$ with $3$ and simplify. I get $(3)^4 + (3) + 2 = 81 + 5 = 86$. So the remainder is 86.

