how to factor completely this problem x^4+3x^2-28

Question

anonymous · Answer

higher degree polynomials you basically use trial and error to find one root and then you use polynomial long division to find the others.

anonymous · Answer

thank for the help mathdood

anonymous · Answer

No problem do you know what to do from here?

anonymous · Answer

yeah kind of i have more question if i don't

anonymous · Answer

Ok well what two numbers multiplied give -28, and added together gives 3? Off the top of my head I would say 7 and -4!

since you have x^4 + 3x^2 - 28, you can also see that x^4 and x^2 are the only polynomials in your expression and x^4 is just the square of x^2. So now we can probably safely assume that the roots will look something like this:

(x^2 + 7) (x^2 - 4).

x^2 + 7 is an irreducible quadratic, but x^2 - 4 can still be reduced. So to factor completely, we just need to factor apart x^2 - 4:

(x^2 + 7) (x^2 - 4)

(x^2 + 7) (x +2) (x-2)

anonymous · Answer

thanks Hermeezey you been a big help