Question

give possible expressions for the lenght breadth nd height of the cuboid whose volume is x3-6x2+11x-6​

Answer 1

Answer:

Volume of a cuboid = L * B * H

Since one side = x-1

& volume = x^3 - 6x² + 11x - 6

So, the product of other 2 sides =

( x^3 - 6x² + 11x - 6) ÷ ( x-1)

= quotient = x² - 5x + 6 & remainder has to zero

Now, by factorizing x² - 5x + 6

= (x-3) ( x- 2)

This way , other 2 sides ( we can say its breadth & height) are ( x-2) & (( x-3)

Answer 2

Question-

Find the length, breadth and height of cuboid whose volume is

x³ - 6x² + 11x - 6​

Answer-

To find the length, breadth and height, we can factorise this volume to get the zeroes. The zeroes we get would be the length, breadth and height.

x³ - 6x² + 11x - 6​

= x³ - (5x² - x²) + (6x + 5x) - 6​

= x³ - 5x² + 6x - x² + 5x - 6

= x(x² - 5x + 6) - 1(x² - 5x + 6)

= (x - 1)(x² - 5x + 6)

= (x - 1)(x² - 2x - 3x + 6)

= (x - 1)(x - 2)(x - 3)

The zeroes are 1, 2 and 3.

Therefore,

Length = 1 unit

Breadth = 2 units

Height = 3 units