The answer is: w = x - 3, h = x - 5
V = l * w * h
V = x³ - 16x² + 79x - 120
l = x - 8
x³ - 16x² + 79x - 120 = (x - 8) * w * h
w * h = (x³ - 16x² + 79x - 120) / (x - 8)
x³ - 16x² + 79x - 120
x - 8 (* x²) | x³ - 8x²
_________________________ (subtract)
-8x² + 79x - 120
x - 8 (* -8x) | -8x² + 64x
_________________________ (subtract)
15x - 120
x - 8 (* 15) | 15x - 120
_________________________ (subtract)
0
w * h = (x³ - 16x² + 79x - 120) / (x - 8) = x² - 8x + 15
Let's find factors of x² - 8x - 15:
x² - 8x - 15 = x² - 3x - 5x + 15
= x * x - 3 * x - (5 * x - 5 * 3)
= x(x - 3) - 5(x - 3)
= (x - 3)(x - 5)
w * h = (x - 3) * (x - 5)
w > h and (x - 3) > (x - 5)
⇒ w = x - 3
h = x - 5