The volume of a rectangular prism is represented by the function x3 + 11x2 + 20x – 32. the width of the box is x – 1 while the height is x + 8. find the expression representing the length of the box

The length of the box is (x+4).

Step-by-step explanation:

The volume of a rectangular prism is represented by the function

Rewrite the given function in factored form.

It is given that the width of the box is x – 1 while the height is x + 8.

The volume of a rectangular prism is

where, l is length, b is width and h is height.

Divide both sides by bh.

Substitute the value of volume, height and width.

Cancel out the common factors.

Therefore the length of the box is (x+4).

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)