## anonymous 5 years ago Factor f(x) = x^4 + 5x^2 - 14 completely.

1. anonymous

let y = x^2 ; it won't factor any further than two quadratics in y.

2. anonymous

The answer is supposed to look something like (this probably isnt the answer but for example) : $(x - \sqrt{7})(x - \sqrt{7})(x + \sqrt{2}i)(x- \sqrt{2}i)$

3. anonymous

Im not sure how to solve for it this way :(

4. anonymous

If you go that far, then so be-it. HOWEVER, if you want it in that form (I normally don't) who am I to stop you. First, factor f(x) into two quadratics: Let y = x^2 => f(x) = y^2 + 5y - 14 = (y+7)(y-2) => f(x) = (x^2+7)(x^2-2) Then you can factorise these (well, if you call using imaginary numbers factorising :@)

5. anonymous

I got $(x + \sqrt{7}i)(x-\sqrt{7}i)(x+\sqrt{2})(x-\sqrt{2})$ does that seem right you?

6. anonymous

I got $(x + \sqrt{7}i)(x-\sqrt{7}i)(x+\sqrt{2})(x-\sqrt{2})$ does that seem right you?