Synthetic division is a method for dividing a polynomial by a linear factor. It involves writing the coefficients of the terms being divided, drawing a box around the number being divided by with a line below, then repeatedly bringing down the next term and performing multiplication and subtraction until reaching a remainder. For example, to divide (2x-7) by (x=3), write the coefficients 2 and 7, box the 3 with a line below, bring down the 3 and multiply and subtract repeatedly to reach a remainder.