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What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

$box enclose bold Volume bold space bold colon bold space bold 3 bold x to the power of bold 2 bold minus bold 12 bold x end enclose$

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217.
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

$box enclose bold Volume bold space bold colon bold space bold 12 bold ky to the power of bold 2 bold plus bold 8 bold ky bold minus bold 20 bold k end enclose$

12ky² + 8ky - 20k
= 4k(3y² + 2y - 5)
= 4k(3y² + 5y - 3y - 5)
= 4k{y(3y + 5) - 1(3y +5)}
= 4k(3y + 5)(y - 1)
∴ The possible expressions for the dimensions of the cuboid are 4k, 3y + 5 and y - 1.

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