What are the possible expressions for the dimension of the cuboids whose volumes are given as in image?

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Solution

(i)
$3 x^{2} - 12 x = 3 x (x - 4)$
$= 3 \times x \times (x - 4)$ ,
The possible values of dimensions are $3, x$ and $x - 4.$

(ii)
$12 k y^{2} + 8 k y - 20 k$
$= 4 k (3 y^{2} + 2 y - 5)$
$= 4 k (3 y^{2} + 5 y - 3 y + 5)$
$= 4 k {y (3 y + 5) - 1 (3 y + 5)}$
$= 4 k (3 y + 5) (y - 1)$
The possible values of dimensions are $4 k$ , $(3 y + 5)$ and $(y - 1) .$

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Similar questions

3 x^{3} - 12 x

3 x^{2} - 12 x

What are the possible expressions for the dimensions of the cuboid whose volumes are given below?
(i) Volume: ${3 x}^{2} - 12 x$

(ii) Volume: $12 k y^{2} + 8 k y - 20 k$

12 k y^{2} + 8 k y - 20 k

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