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beetle2
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Homework Statement
Write [itex]P(x) = x^3+2x+3 [/itex] as the product of Irreducible Polynomials over [itex]Z_5[/itex]
Homework Equations
Polynomial division
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?