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:

angles 1 and 3 are vertical angles, meaning that they are equal to each other. to solve this you may set angle 1 and 3 equal to each other and just solve for x like

110 = 2x + 10

100 = 2x

50 = x

check:

110 = 2* 50 + 10

110 = 100 + 10

110 = 110

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step-by-step explanation: