Long division is used to divide polynomials when the divisor is more complex than a single term. It works similarly to long hand division with numbers, but uses variables instead. Synthetic division is a shortcut method used to divide a polynomial by a linear factor, to find the zeros or roots of a polynomial. It involves writing only the coefficients of the polynomial inside a upside down division symbol and placing the linear factor being tested as a zero on the left before performing the division steps. Both long division and synthetic division can be used to find the quotient when dividing polynomials.