how is the divisor decided lin synthetic division?

Answer 1

Divisor (x - a) , use (a) as divisor

Divisor (x + a) = x - (- a) , use (- a) as divisor.

Divisor ax - b = a(x - b/a) , use (b/a)
as divisor.

Divisor ax + b = ax - (- b) = a [x - (- b/a) ] ,
use (- b /a ) as divisor.

Answer 2

So your question is how will you know the divisor when using synthetic division..right?

I'll give an example..

1.) x+3/x-4

Your divisor is x-4. To get what number should be used in synthetic division, equate the divisor to zero.

x-4=0

then, solve for x.

x=4 (transposed 4 to the other side)

2.) x+3/2x+5

just the same procedure.

=>2x+5=0
=>2x= -5
=>x= -5/2 (divided both sides by 2)

so, the divisor you are going to use in synthetic is -5/2

=D hope i helped...

there are also cases when the divisor has 2 values.. when x is squared...