# Thread: Need help factoring and graphing a quartic function

1. ## Need help factoring and graphing a quartic function

Here's the function.
x^4-2x^3+2x-1 (Hint: X=1 is a triple root)

Could anyone give me an explanation on how to factor this?

Also,how would I graph this? I don't understand how to graph cubic and quartic functions. An explanation here or from a website would probably suffice. Thank you very much for your time in reading this problem.

2. Hello, RaphaelB30!

$y \:=\:x^4-2x^3+2x-1$ . . (Hint: $x=1$ is a triple root.)

Could anyone give me an explanation on how to factor this?
That was a BIG hint!

If $x = 1$ is a triple root,
. . then the function is divisible by: $(x-1)^3 \:=\:x^3 - 3x^2 + 3x - 1$

Using long division: . $y \;=\;(x^3-3x^2+3x-1)(x+1) \;=\;(x-1)^3(x+1)$

3. I'll throw in my two cents.. Someone else will do better though

You need to use synthetic division to factor first. Once you have the equation down to a few smaller bits and pieces, then you can analyze it more thoroughly to find the x-intercepts, and then from there, you can sub in numbers to determine where the graph will be positive or negative.

In the case of your question, you are told that there is a triple root at x=1 .... so it factors to (x-1)(x-1)(x-1) .... or (x-1)^3 .... and then one more part that you will need to use synthetic division to find.

But someone else will be of more help :P I just wanted to exercise my explaining ability on the math that I've learned this year .