Elementary Geometry for College Students (7th Edition)

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: 11

Answer

$x^2+5x-24 = (x+8)~(x-3)$

Work Step by Step

Let's consider a trinomial in this form: $~x^2+bx+c$ To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = c$ Then we can factor the trinomial as follows: $~x^2+bx+c = (x+r)~(x+s)$ Let's consider this trinomial: $~x^2+5x-24$ To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = 5$ and $r\times s = -24$. We can see that $(8)+(-3) = 5~$ and $(8)\times (-3) = -24$ We can factor the trinomial as follows: $x^2+5x-24 = (x+8)~(x-3)$
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