Question

the volume of a cuboid is polynomial p[x]=8x3+12x2-2x-3 find possible expression for dimensions of cuboid verify result by taking x=5units

Answer 1

Answer:

The dimension are 11 , 9 , 13

Step-by-step explanation:

Given : The volume of a cuboid is polynomial $p(x)=8x^3+12x^2-2x-3$

To find : Possible expression for dimensions of cuboid and verify result by taking x=5 units.

Solution :

Volume is the factorized as:

$p(x)=8x^3+12x^2-2x-3$

$p(x)=8x^3-2x+12x^2-3$

$p(x)=2x(4x^2-1)+3(4x^2-1)$

$p(x)=(4x^2-1)+(2x+3)$

$p(x)=2x+1)(2x-1)(2x+3)$

Now, The possible dimension are

(2x+1) , (2x-1) , (2x+3)

Verification :

If x=5

(2x+1)=2(5)+1=11

(2x-1)=2(5)-1=9

(2x+3)=2(5)+3=13

Hence the dimension are 11 , 9 , 13

Volume of the cuboid with dimensions,

$V=11\times 9\times 13=1287$

Now, substitute x=5 in the given function,

$p(x)=8x^3+12x^2-2x-3$

$p(5)=8(5)^3+12(5)^2-2(5)-3$

$p(5)=1000+300-13$

$p(5)=1287$

So, Both the volumes are equal it is verified.

Answer 2

Answer:

Answer:

The dimension are 11 , 9 , 13

Step-by-step explanation:

Step-by-step explanation:

Given : The volume of a cuboid is polynomial  

To find : Possible expression for dimensions of cuboid and verify result by taking x=5 units.

Solution :

Volume is the factorized as:

Now, The possible dimension are

(2x+1) , (2x-1) , (2x+3)

Verification :

If x=5

(2x+1)=2(5)+1=11

(2x-1)=2(5)-1=9

(2x+3)=2(5)+3=13

Hence the dimension are 11 , 9 , 13

Volume of the cuboid with dimensions,

Now, substitute x=5 in the given function,

So, Both the volumes are equal it is verified