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Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
Chapter Closure
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Exercise 126 Page 138

a An area model has the shape of a rectangle, which means its area is calculated by multiplying its length and width.
If x(3x-2) is the area of the model, one factor must represent the width and the other represents the length.

By separating the sum contained within the second factor, we can create two smaller rectangles within the model.

Let's perform the multiplications.

Since the product of the model's sides and the sum of the smaller rectangle's area both describe the same thing, we can equate these expressions. x(3x-2)=3x^2-2x

b Like in Part A, we will create an area model by letting (x+1) and (x+2) represent the dimensions of the rectangle.
By separating the sum contained within each factor, we can create four smaller rectangles within the area model.

Let's perform the multiplications.

Since the product of the sides and the sum of the smaller rectangle's area both describe the model's area, we can equate these expressions. (x+1)(x+2)=x^2+x+2x+2 ⇕ (x+1)(x+2)=x^2+3x+2

c Like in previous parts, we will create an area model by letting (3x+1) and (x-2) represent the width and length of the model.
By separating the sum contained within each factor, we can create four smaller rectangles within the bigger one.

Let's perform the multiplications.

Since the product of the sides and the sum of the smaller rectangle's area both describe the model's area, we can equate these expressions. (3x+1)(x-2)=3x^2+x-6x-2 ⇕ (3x+1)(x-2)=3x^2-5x-2

d Like in previous parts, we will create an area model by letting (x+3) and (x-1) represent the width and length of the rectangle.
By separating the sum contained within each factor, we can create four smaller rectangles within the model.

Let's perform the multiplications.

Since the product of the sides and the sum of the smaller rectangle's area both describe the big model's area, we can equate these expressions. (x+3)(x-1)=x^2-x+3x-3 ⇕ (x+3)(x-1)=x^2+2x-3

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120
Exercises 121 (Page 137)
Exercises 122 (Page 137)
Exercises 123 (Page 138)
Exercises 124 (Page 138)
125
Exercises 126 (Page 138)
Exercises 127 (Page 138)
Exercises 128 (Page 139)
Exercises 129 (Page 139)