19. Establish each of the assertions below: (a) If a is an arbitrary integer, then 6|a(a² + 11). (b) If a is an odd integer, then 24 | a(a² – 1). - [Hint: The square of an odd integer is of the form 8k + 1.] (c) If a and b are odd integers, then 8|(a² – b²). (d) If a is an integer not divisible by 2 or 3, then 24 | (a² + 23). (e) If a is an arbitrary integer, then 360 | a² (a² – 1)(a² – 4).

19. Establish each of the assertions below: (a) If a is an arbitrary integer, then 6|a(a² + 11). (b) If a is an odd integer, then 24 | a(a² – 1). - [Hint: The square of an odd integer is of the form 8k + 1.] (c) If a and b are odd integers, then 8|(a² – b²). (d) If a is an integer not divisible by 2 or 3, then 24 | (a² + 23). (e) If a is an arbitrary integer, then 360 | a² (a² – 1)(a² – 4).

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter5: Factoring Polynomials

Section5.4: Multiplying Binomials Mentally

Problem 49WE

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