Synthetic division is a method for dividing a polynomial by a linear factor. It involves writing the coefficients of the terms in the polynomial, drawing a box around the number being divided by with a line below, then repeatedly bringing down the first term and multiplying and adding until reaching a remainder. For example, to divide (2x-7) by (x=3), write the coefficients 2 and 7, draw a box around the 3 with a line below, then bring down the 3 and multiply and add 2x3=6, 0-6=-6, -6x3=-18, -18-7=-25, until reaching a remainder.