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Thread: Product of irreducible polynomials.

  1. #1
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    Product of irreducible polynomials.

    Let $\displaystyle f(x)=x^3+x^2+x+1 \in Z_{2}[x] $. Write f(x) as a product of irreducible polynomials over $\displaystyle Z_{2}$

    I have $\displaystyle f(x)=(x^2+1)(x+1)$, they both have zeros in $\displaystyle Z_{2}$, is that right?
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Let $\displaystyle f(x)=x^3+x^2+x+1 \in Z_{2}[x] $. Write f(x) as a product of irreducible polynomials over $\displaystyle Z_{2}$

    I have $\displaystyle f(x)=(x^2+1)(x+1)$, they both have zeros in $\displaystyle Z_{2}$, is that right?
    So far correct but $\displaystyle x^2+1 = (x+1)^2$.
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