# Thread: How to factorise expression without sollution?

1. ## How to factorise expression without sollution?

I've got an expression: $\displaystyle x^4+5x^2+6$. How can I factorise it? All methods I know are based on finding one solution and simplifying the expression to (x-a)(...). But this one is always positive, no matter x, so it's not possible here. It's a polynomial of degree 4, so it must be possible to at least make it to the form $\displaystyle a(x^2+bx+c)(x^2+dx+e)$ How can I do that? (only real numbers, please)

2. Are you sure that there are two variables in your expression ($\displaystyle x$ and $\displaystyle s$)? I think they want $\displaystyle \left(2+x^2\right) \left(3+x^2\right)$...

3. Right, that's a typos.
$\displaystyle x^4+5x^2+6$

4. Try look under Application to higher-degree equations.
Quadratic equation - Wikipedia, the free encyclopedia

5. hello
put $\displaystyle x^{2}=u$,and factorize.

6. The problem is that in this way I get $\displaystyle x^2<0$ and I'd rather not mess up with complex numbers.

edit: To be specific: $\displaystyle x^2=-2 \lor x^2=-3$ if I've got it right.

7. ## Re: How to factorise expression without sollution?

take x^2 = a

a^2 + 5a + 6 = 0

solve this simple quadratic eqn and then put the value of a = x^2 and solve further

8. well, $\displaystyle x^4+5x^2+6$ has only complex roots.

9. Originally Posted by Raoh
well, $\displaystyle x^4+5x^2+6$ has only complex roots.
Yes, but as far as I know any polynomial can be written in form of multiplied $\displaystyle (x-a)$ and $\displaystyle (ax^2+bx+c)$ (in this case it would be only the latter). Or at least that's what I was taught.

10. well in $\displaystyle \mathbb{R}$,the only factorization you can get is $\displaystyle (x^2+2) (x^2+3)$.

11. in your $\displaystyle 4^{th}$ post,$\displaystyle (a,b,c) \in \mathbb{R}^{3}$.

12. Originally Posted by Raoh
well in $\displaystyle \mathbb{R}$,the only factorization you can get is $\displaystyle (x^2+2) (x^2+3)$.
Ahh, what a fool I am! That's what I was looking for