i don't know how to factorize it in reals.
Maybe because it can't be factored over the reals?
but i read that all pol. can be factored in reals and the higher power of x can be 2
c,a,d,f =/= 0
X^2 +1=0, this polynominal can be factored over the reals?
All polynomials can be factored in the complex numbers, not the reals.
This has no real roots. Hint: The expression is quadratic in x2.
Isn't that statement equivalent to the Mertens conjecture?
Fundamental theorem of real algebra:
Every monic polynomial can be uniquely factored into a product of monic irreducible polynomials. Any irreducible polynomial is either linear or quadratic.
Guys, he's saying that all polynomials with real coefficients can be factors as (at most) quadratics with real coefficients. This is true.
As the equation has no real roots, you are looking for the product of a pair of quadratics.
You don't need a and d. Since ad=1, you can scale the two polynomials to make a and d equal to 1.
This is the source of your problems. Try again.
Did you read the guidelines? Don't post complete solutions.
Apologies -- got lazy.
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