Let f(x) = x ³ −x−1 ∈ Z₅[x]. Find the product of x ² +2x+1+ (f(x)) and x ² +3x−1+ (f(x)) using the algorithm in page 23, block 1. You should show all the steps as in example 11, page 22, block 1.

Word Count : 231

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Sure, let's break it down step by step.

Firstly, let's define the polynomials:

\[ f(x) = x^3 - x - 1 \in \mathbb{Z}_5[x] \]

And the polynomials:

\[ g(x) = x^2 + 2x + 1 + (f(x)) \]

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Degree : PG DIPLOMA PROGRAMMES
Course Name : Post Graduate Diploma in Early Childhood and Foundational Stage Education
Course Code : PGDECFE
Subject Name : Curriculum and Pedagogy of Early Years and Foundational Stage Education: Part-2
Subject Code : MCD 3
Year : 2023