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(L

^{2}-14L + 48) = 288L

^{3}- 14L^{2}+ 48L - 288 = 0The 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)(L

^{2}- 2L + 24) = 0Using L = 12 we have:

length 12 inches

width 12-6 = 6 inches

height 12-8 = 4 inches

volume 12(6)(4) = 288 in

^{3}From the L

^{2}-2L+24 and using quadratic equationwe find the other roots are complex and thus discardable