# Can you please explain how to factorize

Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)

I like Serena
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Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)
Which complex roots did you get?

Mentallic
Homework Helper

Can you please explain how to factorize x4+2x2+9
If i do it by quadratic formula, i get complex roots ... in my book, it has been factorized to
(x2+2x+3)(x2-2x + 3)
When it says factorize over the reals, it means your factors have to have real coefficients. A root of x-(a+bi) does not have all real coefficients. Also remember that any real quadratic with a complex root also has a complex conjugate as its other root. So you can also work backwards from the two conjugates to find the real quadratic that has those roots.

your equation can be written as
X4 + 6X2 - 4X2 + 9
= X4 + 6X2+9 - 4X2
= ( X2 + 3 )2 - (2X)2
= ( X2+3+2X) (X2+3- 2X)

Last edited:
mathman