# Thread: Zeros and end behaviour polynomial curve

1. ## Zeros and end behaviour polynomial curve

Okay, so it's exam review time... long story short, I remember a couple of methods of finding the zeros of a polynomial function. One is by using my calculator :P if it's cubic or quadratic.

The other was to use the synthetic division, and another: long division.

I have a feeling I'm missing something here. Could you guys help me out. The review question is:

States the zeros and end behaviour of the following function:

f(x)= 2x^3 + 3x^2 - x + 2

2. Originally Posted by mike_302
Okay, so it's exam review time... long story short, I remember a couple of methods of finding the zeros of a polynomial function. One is by using my calculator :P if it's cubic or quadratic.

The other was to use the synthetic division, and another: long division.

I have a feeling I'm missing something here. Could you guys help me out. The review question is:

States the zeros and end behaviour of the following function:

f(x)= 2x^3 + 3x^2 - x + 2
I'm afraid there isn't really any special hints and tips apart from trying out a few values until you get a zero!

For example, you get a zero for $x = -2$. Which means that $x+2$ is a factor.

Use long division, or indeed synthetic division, to divide $2x^2+3x^2-x+2$ by $(x+2)$, and the result will be a quadratic of the form $ax^2+bx+c$

Then simply write the function as $f(x) = (x+2)(ax^2+bx+c) = 0$ ... and then use normal quadratic methods to factorise the quadratic and find the other two roots! (or use the quadratic formula).