Question

The volume of a cuboid is polynomial P() =8^3 + 12^2 − 2 − 3. Find possible
expressions for dimensions of the cuboid.

Answer 1

Step-by-step explanation:

Given Question:-

The volume of a cuboid is polynomial P() =8^3 + 12^2 − 2 − 3. Find possible expressions for dimensions of the cuboid.

Correct Question :-

The volume of a cuboid is polynomial

P(x) = 8x³ + 12x² - 2x - 3. Find possible the

expressions for dimensions of the cuboid.

Solution :-

Given that :-

The volume of a cuboid is

P(x) = 8x³ + 12x² - 2x - 3

It can be written as

=> P(x) = 4x²(2x+3) -1 (2x+3)

=> P(x) = (2x+3)(4x²-1)

It can be written as

=> P(x) = (2x+3)[(2x)²-1²]

=> P(x) = (2x+3)(2x+1)(2x-1)

Since (a+b)(a-b) = a²-b²

Where a = 2x and b = 1

We know that

Volume of a cuboid = lbh cubic units

=> lbh = (2x+3)(2x+1)(2x-1)

Therefore the dimensions are (2x+3) , (2x+1) and (2x-1)

Answer:-

The possible dimensions of the cuboid for the given problem are (2x+3) , (2x+1) and (2x-1)

Used formulae:-

• Volume of a cuboid = lbh cubic units
• l = length
• b = breadth
• h = height