Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 8 - Polynomials and Factoring - 8-6 Factoring ax(squared) + bx + c - Practice and Problem-Solving Exercises: 36

Answer

The length is (6x+15)

Work Step by Step

Area is Length $\times$ width. The given area is $18x^{2}$ + 69x + 60. And the width is 3x + 4. When we use FOIL to simplify we follow. FOIL: First (Multiply the first variables in the brackets), outside (Multiply the outer variables), Inside (Multiply the inside variables), Last (Multiply the last variables in the brackets). So: (ax+b)(cx+d) the number in front of $x^{2}$ is a$\times$ c And since one of the numbers is 3 and the final ac is 18 thus the other number is $\frac{18}{3}$ = 6. The last number in the polynomial is b$\times$ d. And since one of the numbers is 4 and the final bd is 60 thus the other number is $\frac{60}{4}$ = 15. Therefore the length is (6x+15) as it is the other factor.
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