P(3)=2(3)^3-(3)^2-18(3)+9

=0

therefore one factor (x-3)

now divide the original function by that factor, then you get

2x^2+5x-3

factorise the above again then you get:

(2x-1)(x+3)

and so the whole function factorised is

(x-3)(2x-1)(x+3)

to find zeros just equate all of them to zero and find x

eg (x-3)=0

X=3

to graph the polynomial find all the x intercepts again equate all the factors to zero (x-3)(2x-1)(x+3) and find x.

then sub x=0 to find y intercept.

you could also differentiate the original funtion to find the turning points and get a very accurate graph.

This sounds really complicated but its quite simple. it draws from several previously learnt(that you should have learnt =p) concepts and combines them. if you have any problems ask again!

sorry to have to tell you that.

Suggest you look at the following site for help….

http://mathworld.wolfram.com/SyntheticDivision.html

I cannot explain it any better than they can!

Answer would be:(2x-1)(x+3)(x-3)