Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Appendix A - A.4 - Quadratic Equations - Exercises - Page 556: 13

Answer

$6y^2+5y-6 = (3y-2)~(2y+3)$

Work Step by Step

Let's consider a trinomial in this form: $~ax^2+bx+c$ To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = a\times c$ Then the next step is to write the trinomial as follows: $~x^2+bx+c = ax^2+rx+sx+c$ Let's consider this trinomial: $~6y^2+5y-6$ To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = 5$ and $r\times s = -36$. We can see that $(9)+(-4) = 5~$ and $(9)\times (-4) = -36$ We can factor the trinomial as follows: $6y^2+5y-6 = 6y^2+9y - 4y-6$ $6y^2+5y-6 = (6y^2+9y) +(- 4y-6)$ $6y^2+5y-6 = (3y)(2y+3) +(-2)(2y+3)$ $6y^2+5y-6 = (3y-2)~(2y+3)$
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