3) Discuss whether one can factorize the following polynomials using polynomials...

[Jenna]

...with real coefficients:? 3) Discuss whether one can factorize the following polynomials using polynomials with real coefficients:
a) x^2 - 2
b) x^2 + 1.
If possible, factor them. If not, explain why not.

 

[Fazaldin A]

a) x^2 - 2 = (x + sqrt(2))(x - sqrt(2)) are the factors.


b) x^2 + 1 = (x + i)(x - i),
where i = sqrt(-1)

 

[Fazaldin A]

a) x^2 - 2 = (x + sqrt(2))(x - sqrt(2)) are the factors.


b) x^2 + 1 = (x + i)(x - i),
where i = sqrt(-1)