Solve $\mathbb{Q}$[X] /$\mathbb{Q}$[X]($X^3$+$X$) $\cong$ $\mathbb{Q}$ x $\mathbb{Q}$[X]/($X^2$ $+$ $1$)

40 Views Asked by At

I need to solve the following 2 questions:

1) $\mathbb{Q}$$[X]$/$\mathbb{Q}$$[X]$($X^3$+$X$) $\cong$ $\mathbb{Q}$ x $\mathbb{Q}$$[X]$/($X^2$ $+$ $1$)

2) $\mathbb{R}$$[X]$/$\mathbb{R}$$[X]$($X^4$$-$$1$) $\cong$ $\mathbb{R}$ x $\mathbb{R}$ x $\mathbb{C}$

For the second questions I tried the following:

($X^4$$-$$1$) = ($X$$+$$1$)($X$$-$$1$)($X^2$$+$$1$) gives $\cong$ $\mathbb{R}$ x $\mathbb{R}$ x $\mathbb{C}$.

Any help would be grateful. Thanks in advance.