what are the possible expressions for the dimensions of the cuboids whose volumes are given below? i) volume:3x²-12x. ii)volume:12

2 thoughts on “what are the possible expressions for the dimensions of the cuboids whose volumes are given below? i) volume:3x²-12x. ii)volume:12”

1. 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:

   (3×2 – 12x), (1/x), and (x) are possible dimensions of the first cuboid

   (3×2 – 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.

   3×2 – 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

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2. Answer:

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