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Factoring Trinomials NEXT

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Problem 1 Product: x 2 + 6x + 8 Step 1: Place the x 2 model in the upper-left region. NEXT

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Problem 1 Product: x 2 + 6x + 8 Step 2:Place the unit models in the lower-right region. There may be more than one possible configuration. Experiment to determine which configuration will allow the appropriate number of x tiles. NEXT

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Problem 1 Product: x 2 + 6x + 8 Step 3: Determine the number of x models needed to complete the rectangle. This configuration requires 9 x tiles. However, it should only have 6 x tiles. NEXT

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Problem 1 Product: x 2 + 6x + 8 Try another configuration. This configuration requires 6 x tiles. NEXT

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Problem 1 Product: x 2 + 6x + 8 Determine the dimensions. x4 x 2 x + 4 x + 2 x 2 + 6x + 8 = (x + 4)(x + 2) NEXT

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Problem 1 Another perspective: x x 4 2 x2x2 4x4x 2x2x8 Notice the four regions. NEXT

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Problem 1 Lets use the four regions as another way to determine the factors of x 2 + 6x + 8: NEXT

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Problem 1 Step 1: Place x 2 in the upper-left region. Determine the factors of x 2 and label the factors. x2x2 x x Determine the factors of x 2 + 6x + 8: NEXT

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Problem 1 x2x2 Step 2: Place the units in the lower-right region. 8 x x Determine the factors of x 2 + 6x + 8: NEXT

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Problem 1 x2x2 8 Step 3: Determine possible factors (configurations) for the units. x x Determine the factors of x 2 + 6x + 8: NEXT

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Problem 1 x2x2 8 Step 3: Determine possible factors (configurations) for the units. x x 1 8 Determine the factors of x 2 + 6x + 8: NEXT

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Problem 1 x2x2 8 Step 4: Label the dimensions and check the resulting products. x x 1 8 1 8 8x8x x Determine the factors of x 2 + 6x + 8: NEXT

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Problem 1 Determine the factors of x 2 + 6x + 8: x2x2 8 x x 1 8 8x8x x The sum of the two products is 9x. The sum of the two products should be 6x. NEXT Try another configuration.

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Problem 1 x2x2 8 Step 3: Determine possible factors (configurations) for the units. x x Determine the factors of x 2 + 6x + 8: 4 2 NEXT

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Problem 1 Determine the factors of x 2 + 6x + 8: x2x2 8 Step 4: Label the dimensions and check the resulting products. 4 2 x x 2 4 NEXT

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Problem 1 Determine the factors of x 2 + 6x + 8: x2x2 8 x x 2 4 4x4x 2x2x The sum of the two products is 6x. The sum of the two products should be 6x. NEXT This configuration works.

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Problem 1 Determine the factors of x 2 + 6x + 8: x2x2 8 x x 2 4 4x4x 2x Use the dimensions to identify the factors. The factors of x 2 + 6x + 8 are (x + 2)(x + 4). NEXT

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Perimeter Is the sum of the lengths of the sides. When solving a perimeter problem, it is helpful to draw and label a figure to model the region.

Perimeter Is the sum of the lengths of the sides. When solving a perimeter problem, it is helpful to draw and label a figure to model the region.

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