Multiplication of Polynomials

Question 1

The dimensions of the base of Box 1 are:width: x; length: 3width: x; length: x + 3width: x; length: x – 3width: x; length: 3x

Revolt · Accepted Answer

B: width: x; length: x + 3

Question 2

3x3x23x34x

Revolt · Accepted Answer

A: 3x

Question 3

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 . Box 2’s volume will be a . Explain your reasoning.

Revolt · Accepted Answer

monomial

Question 4

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

Revolt · Accepted Answer

C: 3x5

Question 5

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

Revolt · Accepted Answer

1 1 3 5

Question 6

What is the volume of Box 3?

Revolt · Accepted Answer

B: x4 + 4x3 + x2 + 4x

Question 7

Box 3: Length = 4 + xWidth = xHeight = x2 + 1The polynomial that represents the volume of Box 3 has a degree of .

Revolt · Accepted Answer

4

Question 8

Compare the area of the bases. If a base has a greater area, it will take up more space on the shelf.Base area of Box 1: 3x2Base area of Box 2: 4x2 – x Which box is likely to occupy more space on the shelf? Explain. Try substituting different values for x.

Revolt · Accepted Answer

If x = 1, the base areas are the same. But if x is greater than 1, then Box 2 has a greater base area. Therefore, Box 2 is likely to occupy more space on the shelf.

Question 9

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 can hold more cereal. If a box has a greater volume, it 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 (since V2 - V1 = x^4(x - 1) > 0).

Question 10

The dimensions of the base of Box 2 are:width: x; length: 3width: x; length: 4x – 1width: x; length: x – 4width: x; length: 4x + 1

Revolt · Accepted Answer

B: width: x; length: 4x – 1

Multiplication of Polynomials Answers

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