Question

What is the volume of the box expressed as a polynomial?

Answer 1

Answer:

D. $10x^3+27x^2-48x+16$

Step-by-step explanation:

We have been given lengths of a box as: $(2x-1),(5x-4)\text { and }(x+4)$. 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:    

$(2x-1)(5x-4)(x+4)$

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

$(2x-1)(5x-4)=2x*5x-2x*4-1*5x-1*-4$      

$(2x-1)(5x-4)=10x^2-8x-5x+4$      

$(2x-1)(5x-4)=10x^2-13x+4$      

Now we will multiply $(10x^2-13x+4)$ with $(x+4)$.

$(10x^2-13x+4)(x+4)$

$10x^2*x+10x^2*4-13x*x-13x*4+4*x+4*4$

$10x^3+40x^2-13x^2-52x+4x+16$

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

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

Answer 2

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