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

3x3x23x34x

Revolt · Accepted Answer

3x2

Question 4

4x2 – x 4x2 – 14x – 45x – 1

Revolt · Accepted Answer

4x2 – x

Question 5

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.

Revolt · Accepted Answer

Part 1: 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.; 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.

Question 6

Explain your reasoning.

Revolt · Accepted 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.

Question 7

Which did you include in your response?

Revolt · Accepted Answer

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.

Question 8

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

Revolt · Accepted Answer

3x5

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

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 because (4x^5 - x^4) - 3x^5 = x^4(x - 1) > 0 when x > 1.

Multiplication of Polynomials Answers

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