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What is the volume of the box expressed as a polynomial?
2x-1 5x-4 x+4

A.) 10x^2 - 32x + 4
B.) 10x^3 - 27x^2 - 32x + 16
C.) 10x^3 - 16
D.) 10x^3 + 27x^2 - 48x + 16

Answer :

You have to multiply the polynomials by each other:
(2x-1) * (5x-4) =10x^2-13x+4
(10x^2-13x+4)(x+4)=

10x^3+27x^2-48x+16

Answer:

D. [tex]10x^3+27x^2-48x+16[/tex]

Step-by-step explanation:

We have been given lengths of a box as: [tex](2x-1),(5x-4)\text { and }(x+4)[/tex]. We are asked to find the volume of our given box.

Since all the sides of box are not equal, therefore, our box is a rectangular box.

Since the volume of a rectangular box equals the product of all of its sides, so we will multiply our given sides to find the volume of box as:    

[tex](2x-1)(5x-4)(x+4)[/tex]

First of all we will multiply our first two expressions as:

[tex](2x-1)(5x-4)=2x*5x-2x*4-1*5x-1*-4[/tex]      

[tex](2x-1)(5x-4)=10x^2-8x-5x+4[/tex]      

[tex](2x-1)(5x-4)=10x^2-13x+4[/tex]      

Now we will multiply [tex](10x^2-13x+4)[/tex] with [tex](x+4)[/tex].

[tex](10x^2-13x+4)(x+4)[/tex]

[tex]10x^2*x+10x^2*4-13x*x-13x*4+4*x+4*4[/tex]

[tex]10x^3+40x^2-13x^2-52x+4x+16[/tex]

[tex]10x^3+27x^2-48x+16[/tex]

Therefore, the volume of our given box is [tex]10x^3+27x^2-48x+16[/tex] cubic units and option D is the correct choice.

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