Determine whether or not x3 +2x+1 and x4 +3x-2 are congruent mod
x2 + 2x + 2 in Q[x]. Answer the same question for x4 + x3 + x2 + 2 and x3 + 1
mod(x2 + 1) in Z3[x].
Help please.
If you learn latex, then you will get answers a lot quicker. A quick search on google should get you started along with [*tex][*/tex] boxes. I'm assuming by Q[x] you mean rational numbers, but I don't know what you mean by "Z3[x]" In your own words, explain what it means
We are asked whether or not $\displaystyle x^3+2x+1 \equiv x^4+3x-2 \mod{x^2+2x+2}$ is true in the space of rational numbers.
If this were true then $\displaystyle x^2+2x+2$ divides the difference $\displaystyle (x^4+3x-2) - (x^2+2x+1) = x^4-x^2+x-3$ with a rational quotient and no remainder.
Use polynomial long division to verify whether or not it is the case.
If I'm missing something, let me know.