Question

4. Divide:
(8x³ - 36x² + 54x - 27) by (2x - 3)​

Answer 1

Answer:

The possible side of the cube, a = 2x - 3

Step-by-step explanation:

Given,

The volume of a cube =8x^3-36x^2+54x-27=8x

3

−36x

2

+54x−27

To find, the possible side of the cube = ?

Let the side of the cube = a

We know that,

The volume of the cube =a^{3}=a

3

∴ a^{3} =8x^3-36x^2+54x-27a

3

=8x

3

−36x

2

+54x−27

a^{3} =(2x)^3-3(2x)^2(3)+3(2x)(3^2)-(3)^3a

3

=(2x)

3

−3(2x)

2

(3)+3(2x)(3

2

)−(3)

3

Using the algebraic identity,

(a-b)^{3}=a^{2}-3a^{2}b+3ab^{2}-b^{3}(a−b)

3

=a

2

−3a

2

b+3ab

2

−b

3

Here, a = 2x and b = 3

a^{3} =(2x-3)^3a

3

=(2x−3)

3

⇒ a = 2x -3

Hence, the possible side of the cube, a = 2x - 3

Answer 2

$\huge \underline \mathsf \green{ANSWER}$

$\frac{8 {x}^{3} - 36 {x}^{2} + 54x - 27 }{2x - 3}$

${8x}^{3} - {36x}^{2} + 27 + 9$