Question

What are the possible expressions for the dimensions of the cuboid whose volume is 3x²-12x.

Answer 1

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Problem based on geometrical figure:

First we determine all the factors of the given polynomial by splitting middle term and then consider any of the factor as any of the dimension.

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Solution:

 

(i) Volume : 3x² – 12x

Since, volume is product of length, breadth and height therefore by factorizing the given volume, we can know the length, breadth and height of the cuboid.

3x²– 12x

= 3x(x – 4)

 

Hence,possible expression for length = 3

Possible expression for breadth = x

Possible expression for height = (x – 4)

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Answer 2

$\huge\bold\purple{Answer:-}$

I think you're probably being asked to factor these expressions fully, but really, there are an infinite number of possible expressions for the dimensions. For example: (3x2 - 12x), (1/x), and (x) are possible dimensions of the first cuboid (3x2 - 12x), (x4-19), and (1/(x4-19)) are possible dimensions as well But let's ignore that and just fully factor each expression for volume. 1. 3x2 - 12x 3(x2 - 4x) 3x(x - 4) There are only three factors, so there is only one combination of possible dimensions: 3, x, and (x - 4) 2. 12ky2 + 8ky - 20k 4(3ky2 + 2ky - 5k) 4k(3y2 + 2y - 5) 4k(3y + 5)(y - 1) Now we've got four factors, so there are several combinations of possible dimensions: 4, k, and (3y2 + 2y - 5) 4, (3y + 5), and (ky - k)k, (3y + 5), and (4y - 4) 4, (y - 1), and (3ky + 5k) k, (y - 1), and (12y + 20) (3y + 5), (y - 1), and 4k