Intermediate Algebra chapter 5 part 4

Synthetic Division
Chapter 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