Question

Factor f(x) = x^4 + 5x^2 - 14 completely.

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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 :@)

Answer 5

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

Answer 6

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