
Andrew M. answered 11/03/17
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
Lwh= 288
w = L-6
h = L-8
L(L-6)(L-8) = 288
L(L2-14L + 48) = 288
L3 - 14L2 + 48L - 288 = 0
The possible real roots of the polynomial will be factors of -288
±{1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288}
With synthetic division trying possible roots I found:
12 | 1 -14 48 -288
| 12 -24 288
-----------------------------
1 -2 24 |0
-----
Since the remainder is zero, L=12 is a root and (L-12) is a factor
(L-12)(L2 - 2L + 24) = 0
Using L = 12 we have:
length 12 inches
width 12-6 = 6 inches
height 12-8 = 4 inches
volume 12(6)(4) = 288 in3
From the L2-2L+24 and using quadratic equation
we find the other roots are complex and thus discardable