Lesson 4: Multiplication of Polynomials

Question 1

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 .

Revolt · Accepted Answer

monomial; binomial

Question 2

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

Revolt · Accepted Answer

4x5 – x4

Question 3

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

Revolt · Accepted Answer

3x5

Question 4

Box 2: [image 1] [image 2] Degree of length: [image 3] Degree of width: [image 4] Degree of height: [image 5] Degree of volume:

Revolt · Accepted Answer

Degree of length:: 1; Degree of length:: 3; Degree of length:: 5

Question 5

What is the volume of Box 3?

Revolt · Accepted Answer

x4 + 4x3 + x2 + 4x

Question 6

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 7

The productsumdifferencequotient of the degrees of each factor is the degree of the product.

Revolt · Accepted Answer

sum

Question 8

What is the base area of Box 3?x2 + x

Revolt · Accepted Answer

What is the base area of Box 3?: 1; What is the base area of Box 3?: 4

Question 9

Why does this make sense?

Revolt · Accepted Answer

You use the product of powers law of exponents to combine the exponents; this law says to add the exponents.

Lesson 4: Multiplication of Polynomials Answers

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