Math 101	Intermediate Algebra
Synthetic Division Chapter 5, Sections 5
When Synthetic Division Can Be Used Use synthetic division only when the divisor has the form x - a, where a is some number. How to Do Synthetic Division--Learn by Example Dividend must be written in descending powers of x. Divisor must have the form x - a. Problem:  Divide   x3 + x + 10 x + 2 Write coefficients of dividend on the first line. Notice the 0 for 0x2, which is a missing power of x. Write in a of x - a. Notice x + 2 = x - (-2). Carry 1 down. -2 = -2 · 1. Add 0 and -2 to get -2. 4 = -2 · -2. Add 1 and 4 to get 5. -10 = -2 · 5. Add 10 and -10 to get 0. Completed synthetic division. Quotient is 1x2 + (-2)x + 5. Remainder is 0. Notes x3 + x + 10 = (x + 2)(x2 - 2x + 5) Notice that when the remainder is 0, the divisor and quotient are factors of the dividend, as the above equation shows. Dividend x3 + x + 10 Divisor x + 2 Quotient x2 - 2x + 5 Remainder 0