The volume of a rectangular prism (shown below) is 48x^3+56x^2+16x Answer the following questions: (1) What are the dimensions of the prism?
(2) If x = 2, use the polynomial 48x^3+56x^2+16x to find the volume of the prism.
(3) If x = 2, use the factors found in part a to calculate each dimension.
(4) Using the dimensions found in part c, calculate the volume. Show all work.

(a)

(b)

(c)

(d)

Step-by-step explanation:

Given

Solving (a): The prism dimension

We have:

Factor out 8x

Expand 7x

Factorize

Factor out 3x + 2

So, the dimensions are:

Solving (b): The volume when

We have:

Solving (c): The dimensions when

We have:

Substitute 2 for x

So, we have:

Solving (d), the volume in (c)

We have:

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1