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Discuss the validity of the statement below. If the statement is true, explain why. If not, give a counterexample. If n is a positive integer greater than 1, then un + vn can be factored. Choose the correct answer below. A. The statement is true because un + vn is a perfect square, which can be factored. B. The statement is true. For any n, where n is a positive integer greater than 1, un +vn is factorable because u = - v is a solution to the equation un + v₁ = 0. Therefore, un + vn always has u + v as a factor. C. The statement is false. When n = 2, un + vn is of the form u² + v². This is a known form that is not factorable since u² + v² ± (au + bv)(cu + dv) for any choice of real number coefficients a, b, c, and d. D. The statement is false. When n = -2, un + vn can still be factored. In fact, -2 u2+v² = (u-v)(u + v).

Discuss the validity of the statement below. If the statement is true, explain why. If not, give a counterexample. If n is a positive integer greater than 1, then un + vn can be factored. Choose the correct answer below. A. The statement is true because un + vn is a perfect square, which can be factored. B. The statement is true. For any n, where n is a positive integer greater than 1, un +vn is factorable because u = - v is a solution to the equation un + v₁ = 0. Therefore, un + vn always has u + v as a factor. C. The statement is false. When n = 2, un + vn is of the form u² + v². This is a known form that is not factorable since u² + v² ± (au + bv)(cu + dv) for any choice of real number coefficients a, b, c, and d. D. The statement is false. When n = -2, un + vn can still be factored. In fact, -2 u2+v² = (u-v)(u + v).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Discuss the validity of the statement below. If the statement is true, explain why. If not, give a counterexample. If n is a positive integer greater than 1, then un + vn can be factored. Choose the correct answer below. A. The statement is true because un + vn is a perfect square, which can be factored. B. The statement is true. For any n, where n is a positive integer greater than 1, un +vn is factorable because u = - v is a solution to the equation un + v₁ = 0. Therefore, un + vn always has u + v as a factor. C. The statement is false. When n = 2, un + vn is of the form u² + v². This is a known form that is not factorable since u² + v² ± (au + bv)(cu + dv) for any choice of real number coefficients a, b, c, and d. D. The statement is false. When n = -2, un + vn can still be factored. In fact, -2 u2+v² = (u-v)(u + v).
Transcribed Image Text:Discuss the validity of the statement below. If the statement is true, explain why. If not, give a counterexample. If n is a positive integer greater than 1, then un + vn can be factored. Choose the correct answer below. A. The statement is true because un + vn is a perfect square, which can be factored. B. The statement is true. For any n, where n is a positive integer greater than 1, un +vn is factorable because u = - v is a solution to the equation un + v₁ = 0. Therefore, un + vn always has u + v as a factor. C. The statement is false. When n = 2, un + vn is of the form u² + v². This is a known form that is not factorable since u² + v² ± (au + bv)(cu + dv) for any choice of real number coefficients a, b, c, and d. D. The statement is false. When n = -2, un + vn can still be factored. In fact, -2 u2+v² = (u-v)(u + v).
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