Multiplication of Polynomials

Question 1

The dimensions of the base of Box 1 are:

Revolt · Accepted Answer

width: x; length: 3x

Question 2

The dimensions of the base of Box 2 are:

Revolt · Accepted Answer

width: x; length: 4x – 1

Question 3

Question 4

Revolt · Accepted Answer

3x2

Question 4

Box 1: Dimensions: x by 3x by x3Area of base = x(3x) = 3x2Box 2: Dimensions: x by 4x – 1 by x3Area of base = x(4x – 1) = 4x2 – xComplete the statements about the number of terms in the polynomial representing the volume of each box. Box 1’s volume will be a ⇒ monomial. Box 2’s volume will be a ⇒ binomial. Explain your reasoning.

Revolt · Accepted Answer

Part 1: Box 1's volume is found by multiplying the area of the base (3x^2) by the height (x^3), which results in 3x^5. Since this expression has only one term, it is a monomial. Box 2's volume is found by multiplying its base area (4x^2 - x) by the height (x^3), using the distributive property: x^3(4x^2) - x^3(x) = 4x^5 - x^4. Since this expression has two terms, it is a binomial.

Question 5

Dimensions of Box 1: x by 3x by x3 The volume of Box 1 is given by:

Revolt · Accepted Answer

3x5

Question 6

Suppose Celine wants to choose a box that maximizes the amount of cereal it can hold.Volume of Box 1: 3x5Volume of Box 2: 4x5 – x4If Celine decides the width of the cereal boxes will be greater than 1, which box will hold more cereal? Explain.

Revolt · Accepted Answer

Box 2 will hold more cereal. Since the width x is greater than 1, we can compare the volumes by subtracting Box 1's volume from Box 2's: (4x^5 - x^4) - 3x^5 = x^5 - x^4. For any value of x > 1, x^5 is greater than x^4, making the difference positive. Therefore, Box 2 has a larger volume than Box 1 for all x > 1.

Question 7

Box 2: Degree of length: Degree of width: Degree of height: Degree of volume:

Revolt · Accepted Answer

Part 1: 5

Question 8

Question 10

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4x2 – x

Question 9

Dimensions of Box 2: x by 4x – 1 by x3The volume of Box 2 is given by:

Revolt · Accepted Answer

4x5 – x4

Question 10

Which did you include in your response?

Revolt · Accepted Answer

If a box has a greater volume, it can hold more cereal.; Box 2 can hold more cereal. Although the value of x is unknown, it represents a length, so it must be greater than zero. For any x > 1, the volume of Box 2 is greater than the volume of Box 1.

Multiplication of Polynomials Answers

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