Question

What are the possible expressions for the dimensions of the cuboids whose volumes are given below? Volume : 12ky2 + 8ky – 20k

Answer 1

Step-by-step explanation:

12ky2 + 8ky – 20k

⇒4(3ky2 + 2ky - 5k)

⇒4k(3y2 + 2y - 5)

⇒4k(3y + 5)(y - 1)

 Hence, possible expression for length = 4k

Possible expression for breadth = (3y +5)

Possible expression for height = (y – 1)

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Answer 2

Step-by-step explanation:

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