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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.

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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 class=

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Answer:

The polynomial that represent the volume of the box is [tex]V=(x^{3}+4x^{2}+3x)\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the box is equal to

[tex]V=LWH[/tex]

we have

[tex]L=(x+3)\ in[/tex]

[tex]W=x\ in[/tex]

[tex]H=(x+1)\ in[/tex]

substitute in the formula

[tex]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}[/tex]