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Question A2: When we study case analysis, we will consider the polynomial function p(n) = 2n³ + 3n²+ n. We know from the first week of class that p(n): : 12 +2²+.... + n², and this gives the remarkable fact that the following implication is true: If n is an integer, then 2n³ +3n² +n is a multiple of 6. We will use case analysis, in clase, to verify this fact directly. It is helpful to note that p(n) can be written as a product, since 2n³ +3n² + n = (2n + 1)(n+1)(n). (a) How can you check that the factorization given above is true?

Question A2: When we study case analysis, we will consider the polynomial function p(n) = 2n³ + 3n²+ n. We know from the first week of class that p(n): : 12 +2²+.... + n², and this gives the remarkable fact that the following implication is true: If n is an integer, then 2n³ +3n² +n is a multiple of 6. We will use case analysis, in clase, to verify this fact directly. It is helpful to note that p(n) can be written as a product, since 2n³ +3n² + n = (2n + 1)(n+1)(n). (a) How can you check that the factorization given above is true?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question A2: When we study case analysis, we will consider the polynomial function p(n) = 2n³ + 3n² +n. We know from the first week of class that p(n) = 1² + 2² + . + n², and this gives the remarkable fact that the following implication is true: If n is an integer, then 2n³ +3n² +n is a multiple of 6. We will use case analysis, in clase, to verify this fact directly. It is helpful to note that p(n) can be written as a product, since 2n³ + 3n² + n = (2n + 1)(n + 1)(n). (a) How can you check that the factorization given above is true?
Transcribed Image Text:Question A2: When we study case analysis, we will consider the polynomial function p(n) = 2n³ + 3n² +n. We know from the first week of class that p(n) = 1² + 2² + . + n², and this gives the remarkable fact that the following implication is true: If n is an integer, then 2n³ +3n² +n is a multiple of 6. We will use case analysis, in clase, to verify this fact directly. It is helpful to note that p(n) can be written as a product, since 2n³ + 3n² + n = (2n + 1)(n + 1)(n). (a) How can you check that the factorization given above is true?
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