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215. Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:

$box enclose bold Area bold space bold colon bold space bold 35 bold y to the power of bold 2 bold plus bold 13 bold y bold minus bold 12 end enclose$

35y² + 13y - 12
= 35y² + 28y - 15y - 12
= 7y (5y + 4) - 3(5y + 4)
= (5y + 4)(7y - 3)
∴ The possible expressions for the length and breadth of the rectangle are 7y - 3 and 5y + 4.

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216.

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?

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