The volume of a box is given by v = 2x3-11x2 +10x +8. one side is (x - 4) and another side is (2x + 1).
find the length of the third side.

The length of the third side is ( x - 2 )

Step-by-step explanation:

Volume of a box is the product of its length, width and height.

Volume of box = length × width × height.

One side is (x - 4) and another side is (2x + 1).

These given sides can be either length, height or width.

The volume of a box is given by V = 2x3-11x2 +10x +8. This means each of the sides are factors of the volume. To get the third side, we divide the volume by the product of the two given sides.

Product of the two given sides =

( x-4 ) (2x + 1) = 2x^2 + x - 8x + 4

= 2x^2 - 7x - 4

The long division is shown on the attached photo

The length of the third side is ( x - 2 )

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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