AnswersINMT3 Integrated Math 3 Sem 1 26-27Introduction to Polynomials

Multiplication of Polynomials Answers

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1
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The dimensions of the base of Box 1 are:

A
width: x; length: 3
B
width: x; length: x + 3
C
width: x; length: x – 3
D
width: x; length: 3x
2
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The dimensions of the base of Box 2 are:

A
width: x; length: 3
B
width: x; length: 4x – 1
C
width: x; length: x – 4
D
width: x; length: 4x + 1
3

3x3x23x34x

A
3x
B
3x2
C
3x3
D
4x
4

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.

Answer:

Box 2 will most likely occupy more shelf space. For values of x greater than 1, the base area of Box 2 is greater.

5

Which did you include in your response?

A
Box 2 will most likely occupy more shelf space.
B
For values of x > 1, the base area of Box 2 is greater.
6

Which did you include in your response?

A
Box 1’s volume is modeled by a monomial times a monomial, so it will be a monomial.
B
Box 2’s volume is modeled by a monomial times a binomial, so it will be a binomial.
7

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

A
3x7
B
3x6
C
3x5
D
5x3
8

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.

Answer:

Box 2 can hold more cereal because (4x^5 - x^4) - 3x^5 = x^4(x - 1) > 0 when x > 1.

9

Which did you include in your response?

A
If a box has a greater volume, it can hold more cereal.
B
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.
10

The product✔ sumdifferencequotient of the degrees of each factor is the degree of the product.

A
product
B
✔ sum
C
difference
D
quotient
11

Why does this make sense?

A
You use the power of a product law of exponents to combine the exponents; this law says to add the exponents.
B
You use the power of a power law of exponents to combine the exponents; this law says to multiply the exponents.
C
You use the product of powers law of exponents to combine the exponents; this law says to add the exponents.
12

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

Answer:

4

13

What is the volume of Box 3?

A
4x3 + 2x2 + 4x + 1
B
x4 + 4x3 + x2 + 4x
C
x4 + 4x3 + 2x2 + 4x
D
x4 + 2x3 + x2 + 4
14

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.

Question illustration
Answers:
Blank 1:monomial
Blank 2:binomial
15

4x2 – x 4x2 – 14x – 45x – 1

A
4x2 – x
B
4x2 – 1
C
4x – 4
D
5x – 1
16

Explain your reasoning.

Answer:

Box 1’s volume is 3x^5, which is a monomial because it has one term. Box 2’s volume is 4x^5 − x^4, which is a binomial because it has two terms. Box 1 is modeled by a monomial times a monomial, while Box 2 is modeled by a monomial times a binomial.

17

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

A
4x5 – x4
B
4x6 – x3
C
4x5 + x4
D
x3 + 5x –1

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