Question

Alena is packing a box that has a height of one inch more than the width and a length of three inches more than the width, as shown in the diagram below. Write a polynomial expression, In simplified form, that represents the volume of the box.

(I need help...)

Answer 1

The polynomial that represent the volume of the box is
`V=(x^(3)+4x^(2)+3x)\ in^(3)`

Explanation:

we know that

The volume of the box is equal to

`V=LWH`

we have

`L=(x+3)\ in`

`W=x\ in`

`H=(x+1)\ in`

substitute in the formula

`V=(x+3)(x)(x+1)\\V=(x^(2) +3x)(x+1)\\V=x^(3)+x^(2) +3x^(2) +3x\\ V=(x^(3)+4x^(2)+3x)\ in^(3)`