(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Write [itex]P(x) = x^3+2x+3 [/itex] as the product of Irreducible Polynomials over [itex]Z_5[/itex]

2. Relevant equations

Polynomial division

3. The attempt at a solution

I start out by taking out a factor of [itex]x+3[/itex]

That is

[itex]x+3 \div x^3+2x+3 [/itex]

I get [itex]P(x) = x^2-3x+1 [/itex] which has zero remainder mod 5.

Is the product of irreducible polynomial [itex](x+3) (x^2-3x+1) [/itex]

or do I reduce [itex]P(x) = x^2-3x+1 [/itex] by taking out a factor of x+1 ie

[itex]x+1 \div x^2-3x+1 [/itex]

I know the irreducible polynomials coefficients should add up to the original degree ,So I have one with degree 1 and the second with degree 2.

am I on the right track?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Irreducible Polynomials

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