Multiplication of Polynomials Answers
The dimensions of the base of Box 1 are:
The dimensions of the base of Box 2 are:
Which did you include in your response?
3x3x23x34x
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 .
Why does this make sense?
Box 2: [image 1] [image 2] Degree of length: [image 3] Degree of width: [image 4] Degree of height: [image 5] Degree of volume:
The productsumdifferencequotient of the degrees of each factor is the degree of the product.
What is the volume of Box 3?
What is the base area of Box 3?x2 + x
The dimensions of the base of Box 1 are:
3x3x23x34x
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 will hold more cereal. To compare the two volumes, subtract the volume of Box 1 from the volume of Box 2: $(4x^5 - x^4) - (3x^5) = x^5 - x^4$. Since Celine decided that the width, $x$, will be greater than 1, $x^5$ will always be greater than $x^4$. This makes the difference $(x^5 - x^4)$ a positive value, meaning Box 2's volume is greater than Box 1's volume for all $x > 1$.
Why does this make sense?
What is the volume of Box 3?
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