How do you write a polynomial that represents the volume

Sergio Bradshaw

Sergio Bradshaw

Answered question

2022-02-04

How do you write a polynomial that represents the volume of a box that is a rectangular prism has the dimensions length x+6, width x2, and height x1?

Answer & Explanation

arrejuntam58

arrejuntam58

Beginner2022-02-05Added 11 answers

Step 1
The volume of a rectangular prism is simply the product of its three dimensions: in your case, the volume of the prism is, given x.
(x+6)(x2)(x1)
A polynomial is a sum (with some coefficients) of powers of x, so, if we expand the product just written, we have
((x+6)(x2))(x1)=
(x22x+6x12)(x1)=
(x2+4x12)(x1)=
x3+4x212xx24x+12=
x3+3x216x+12
Which is a polynomial, and expresses the volume of the prism

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