Answer: x - 4
The missing dimension of the prism is A
because the volume of the rectangular prism equals the product of the sides, we have:
V = (x - 1)(x - 3)A
but V = x³ - 8x² + 19x - 12
=> x³ - 8x² + 19x - 12 = (x - 1 )(x - 3)A
⇔ x²(x - 1) - 7x(x - 1) + 12(x - 1) = (x - 1)(x - 3)A
⇔ (x² - 7x + 12)(x - 1) = (x - 1)(x - 3)A
⇔ (x² - 3x - 4x + 12)(x - 1) = (x - 1)(x - 3)A
⇔ (x - 3)(x - 4)(x - 1) = (x - 1)(x - 3)A
⇒ A = x - 4
Explanation: