Algebraic long division
Divide the largest term of the divisor into the largest term of the numerator and proceed as normal.
Polynomial remainder theorem for polynomial \(p\left(x\right)\) for first-degree divisors e.g. \(x-3\): \(\frac{p\left(x\right)}{\left(x-a\right)}=p\left(a\right)\) is remainder
Find if some first-degree polynomial e.g. \(x-3\) is a factor of some polynomial \(p\left(x\right)\): check \(p\left(a\right)=0\) (remainder is 0)