Synthetic or Organic?

No we are not talking about food or hair products. We are discussing a quick and nifty way to solving polynomial equations.

I shall not waste your time, so let's get down to solving this.

There are 3 methods to solving this; the first part is the same for all 3 methods. You try random values of x, such as -1, 0 or 1 and see which gets you zero.

In this case, if you used x=1, then 2+5-11+4=0. And wah la!, (x-1) is a factor.

Note: if you subbed x=? and that ? makes your equation ZERO, then (x-?) is a factor.

Now this is where things start to differ.

Method 1: Solving by Long division

Method 2: Synthetic

The solution is, x=1 or x=1/2 or x=-4 (Ans)