Synthetic division is a shortcut method for dividing a polynomial by a simple divisor of the form (x - n). The divisor must be of that form in order for synthetic division to work. If it's not, you'll have to use long division.
If you are given, say, the polynomial equation y = x2+ 5x + 6, you can factor the polynomial as y = (x + 3)(x + 2). Then you can find the zeroes of y by setting each factor equal to zero and solving. You will find that x = –2 and x = –3 are the two zeroes of y.
Synthetic division uses only the coefficients of a polynomial, or the constants in front of each x-term, so it saves a ton of writing compared to using long division of polynomials.
