Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.4 - Factoring Special Forms - Exercise Set - Page 454: 57



Work Step by Step

RECALL: A perfect square trinomial can be factored using either of the following formulas: (i) $a^2+2ab+b^2= (a+b)^2$ (ii) $a^2-2ab+b^2=(a-b)^2$ The given trinomial can be written as: $=x^2-10x + 10^2$ This trinomial is not in the same form as either of the perfect square trinomials in formulas (i) and (ii). Thus, the given trinomial is not a perfect square trinomial so it cannot be factored using formulas (i) and (ii). The trinomial cannot be factored because 100 has no factors whose sum is equal to the numerical coefficient of the middle term. Therefore the given trinomial is prime.
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