Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-3 Multiplying Binomials - Apply What You've Learned - Page 503: c


Please see "work step-by-step" for full sample answer.

Work Step by Step

To check, take a value for x, such as x=4 ft. (I take this value because one side is going to be 10 ft, and multiplying with 10 is easy) Then, the dimensions of Kelly's plot are (10)$\times$(6), the area 60 f$t^{2}$. Substituting x=4 into the polynomial $x^{2}+8x+12$, which we arrived at in part (a), $(4)^{2}+8(4)+12=16+32+12=60,$ we get the same area, so it checks out well. Do the same for Roberto's plot. Take x=4, Dimensions: (10)$\times$(7), Area = 70. Polynomial ($x^{2}+9x+18$) value when x=4: $4^{2}+9(4)+18=16+36+18 = 70.... $ so, this is also OK.
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