$(9$ points$)$ Consider the CRC scheme. Assume G$($X$)=$X$^4+$X$^3+$X$^2+$X$.$

Is it possible to detect any single error in transmission? Explain clearly $($yes$$ or a $$no$$

answer is not sufficient$)$

Suppose during transmission some errors have occurred. The error polynomial is:

E$($X$)=$X$^6+$X$^3+$X

Is the receiver able to detect the error? Explain clearly $($yes$$ or a $$no$$ answer is not sufficient$)$