Question

Calculate (2x+3)(3x+4) in Z5[x].

Answer 1

Answer on Question #48368 – Math – Abstract Algebra:

Calculate $(2x + 3)(3x + 4)$ in $\mathbb{Z}_5[x]$.

Solution.

$$(2x + 3)(3x + 4) = 6x^2 + 8x + 9x + 12 = 6x^2 + 17x + 12;$$ $$6 \equiv 1 \pmod{5};$$ $$17 \equiv 2 \pmod{5};$$ $$12 \equiv 2 \pmod{5};$$

Hence:

$$6x^2 + 17x + 12 = x^2 + 2x + 2 \text{ in } \mathbb{Z}_5[x].$$

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