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 6.3 - Factoring Trinomials Whose Leading Coefficient is Not 1 - Concept and Vocabulary Check - Page 443: 3

Answer

Fill the blank with $-4.$

Work Step by Step

$ax^{2}+bx+c=(F_{1}x+L_{1})(F_{2}x+L_{2})$ FOIL: (F)irst, (L)ast...Outers: $F_{1}$and $L_{2},$ Inners=$ L_{1}$ and $F_{2}$ The product of Firsts is $ax^{2}$ The product of Lasts is $c$ The sum of Outside product and Inside product is $b$ --- The product of Firsts is $12x^{2}\qquad(OK)$ The product of Lasts is $-20$ ... for this to work, the last term in the second parentheses should be $-4.$ Proposed factorization: $(4x+5)(3x-4)$ The sum of Outside product and Inside product is $-10$ If $L_{2}=-4, \qquad 4(-4)+(5)(3)= -1\qquad ... (OK)$ Fill the blank with $-4.$
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