Box 1: Dimensions: x by 3x by x3 Area of base = x(3x) = 3x2 Box 2: Dimensions: x by 4x – 1 by x3 Area of base = x(4x – 1) = 4x2 – x Complete the statements about the number of terms in the polynomial representing the volume of each box. Box 1's volume will be a Box 2's volume will be a . Explain your reasoning.

Box 1’s volume is modeled by a monomial times a monomial, so it will be a monomial. Box 2’s volume is modeled by a monomial times a binomial, so it will be a binomial.

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MrRoyal MrRoyal · Answer 2 · 2021-09-18T10:42:26+02:00

The volume of a box is the amount of space it can occupy.

Box 1's volume will be a monomial
Box 2's volume will be a binomial

The given parameters are:

Dimensions of box 1: x by 3x by x^3

Dimensions of box 2: x by 4x - 1 by x^3

The volume of the box is calculated by multiplying the dimensions.

So, we have:

Box 1

[tex]V_1 = x \times 3x \times x^3[/tex]

[tex]V_1 = 3x^5[/tex]

Box 2

[tex]V_2 = x \times (4x - 1) \times x^3[/tex]

[tex]V_2 = (4x - 1) \times x^4[/tex]

Open brackets

[tex]V_2 = 4x^5 - x^4[/tex]

After calculating the volumes, we have:

[tex]V_1 = 3x^5[/tex] ---- box 1

[tex]V_2 = 4x^5 - x^4[/tex] ---- box 2

Hence,

The volume of box 1 is monomial, because it has 1 term
The volume of box 2 is binomial, because it has 2 terms