# Basic algebra question

1. Apr 12, 2008

### Benzoate

1. The problem statement, all variables and given/known data

Not sure how to factor this equation:

x^4-x^3-x^2+4=0
btw , I do not have a TI 83 calculator

2. Apr 12, 2008

### th3plan

lol this isnt a simple equation to factor its a 4 exponent polynomial, good luck with that, but there is a method i learn in college, dont remember though

3. Apr 12, 2008

### RyanSchw

I'd be curious to know this as well; if I had to guess I’d say that is has no factors given that the graph never crosses the x-axis. I dunno =(

4. Apr 13, 2008

### physixguru

observe the degradation in powers carefully...

5. Apr 13, 2008

### Kurret

It doesnt have any real factors, since:
$$x^4-x^3-x^2+4=(x^2-\frac{x}{2}-\frac{6}{8})^2+~(\frac{x}{2}-\frac{6}{8})^2+\frac{184}{64} > 0$$
:)

6. Apr 13, 2008

### tiny-tim

But every real quartic equation has real quadratic factors (because the complex roots come in conjugate pairs):

(x² + ax + b)(x² + cx + d)

7. Apr 13, 2008

### Kurret

uhm didnt know that! but i mistyped a little, i meant real roots, not real factors.