### Instruction: Find the remainder when $x^4 +x + 2$ is divided by $x-3$.### Response: 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 $(3)^4 + (3) + 2 = 81 + 5 = 86$.