# How to factor this polynomial

1. Dec 7, 2005

### Chocolaty

f(t) = t^3 - 6t^2 +9t + 2

f(1) is not equal to 0
f(-1) is not equal to 0
f(2) is not equal to 0
f(-2) is not equal to 0
No common factor, can't group either

How can I work this one out?
thx

2. Dec 7, 2005

### Galileo

Here's something to remember.
If f=a_0+a_1x+...+a_n x^n is a polynomial with integer coefficients of degree >=1 and q=b/c (ggd(b,c)=1) is a rational root, then b|a_0 and c|a_n.
So the possible rational roots of your polynomial are $\pm 2$, which not roots. This means there are no rational roots so it's a nasty polynomial. :yuck:

3. Dec 7, 2005

### westdavi

I don't believe this is factorable

4. Dec 7, 2005

### matt grime

Of course it's factorable, over some field, it's just that the roots aren't integers (or rational). There's even a formula for the roots. try googling for it.