Question

write possible expressions for the length and breadth of the rectangle whose area is 25asquare -35a+12​

Answer 1

(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