In the ring Z[a], let I = (x³ – 8). (a) Let f(x) = 4.x³ + 6x4 – 2x³ +x² – 8x +3 € Z[r]. Find a polynomial p(x) E Z[r] such that deg p(x)

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In the ring Z[a], let I = (x³ – 8).<br>(a) Let f(x) = 4.x³ + 6x4 – 2x³ +x² – 8x +3 € Z[r]. Find a polynomial p(x) E Z[r] such that<br>deg p(x) < 2 and f(x) = p(x) (mod I).<br>(b) Prove that the quotient ring Z[r]/I is not an integral domain.<br>

Extracted text: In the ring Z[a], let I = (x³ – 8). (a) Let f(x) = 4.x³ + 6x4 – 2x³ +x² – 8x +3 € Z[r]. Find a polynomial p(x) E Z[r] such that deg p(x) < 2="" and="" f(x)="p(x)" (mod="" i).="" (b)="" prove="" that="" the="" quotient="" ring="" z[r]/i="" is="" not="" an="" integral="">

Jun 04, 2022

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In the ring Z[a], let I = (x³ – 8). (a) Let f(x) = 4.x³ + 6x4 – 2x³ +x² – 8x +3 € Z[r]. Find a polynomial p(x) E Z[r] such that deg p(x)

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