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: 58

Answer

prime

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: $=x^2-7x + 7^2$ 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 $49$ 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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