Question

The volume of a cuboid is \( x^3 - 7x + 6 \), then the longest side of the cuboid is:

• A. None of these
• B. \( x - 1 \)
• C. \( x + 3 \)
• D. \( x - 2 \)

Hint:

When dealing with volumes and factorization problems, always attempt to factor the polynomial expression to identify the dimensions of the cuboid.

Answer 1

The Correct Option is C

The volume of a cuboid is given by the formula: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \] We are given the volume expression \( x^3 - 7x + 6 \), which factors as: \[ x^3 - 7x + 6 = (x - 1)(x^2 + x - 6) \] We can factor \( x^2 + x - 6 \) as: \[ x^2 + x - 6 = (x + 3)(x - 2) \] Thus, the factorization of the volume expression is: \[ x^3 - 7x + 6 = (x - 1)(x - 2)(x + 3) \] The longest side of the cuboid is the largest factor, which is \( x + 3 \). Therefore, the correct answer is \( x + 3 \).