Answered

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

Verified Answer :

friedalafiesta

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. \(10x^3+27x^2-48x+16\)

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.

Related Questions