Multiplication of Polynomials Answers
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.
Box 2 will most likely occupy more shelf space. For values of x greater than 1, the base area of Box 2 is greater.
Explain your reasoning.
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.
Which did you include in your response?
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 .
Which did you include in your response?
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.
Box 2 can hold more cereal because (4x^5 - x^4) - 3x^5 = x^4(x - 1) > 0 when x > 1.
Which did you include in your response?
Box 2: Degree of length: Degree of width: Degree of height: Degree of volume:
The product✔ sumdifferencequotient of the degrees of each factor is the degree of the product.
Why does this make sense?
What is the base area of Box 3?x2 + x
What is the volume of Box 3?
Dimensions of Box 2: x by 4x – 1 by x3The volume of Box 2 is given by:
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