Factoring Trinomials

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Problem 1

Product: x2 + 6x + 8Step 1: Place the x2 model in the upper-left region.

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Problem 1

Product: x2 + 6x + 8Step 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.

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Problem 1

Product: x2 + 6x + 8Step 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.

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Problem 1

Product: x2 + 6x + 8Try another configuration.

This configuration requires 6 x tiles.

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Problem 1

Product: x2 + 6x + 8Determine the dimensions.

x 4

x

2

x + 4

x + 2 x2 + 6x + 8 = (x + 4)(x + 2)NEXT

Problem 1Another perspective:

x

x

4

2

x2 4x

2x 8

Notice the four regions.

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Problem 1Let’s use the four regions as another way to determine the factors of x2 + 6x + 8:

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Problem 1

Step 1: Place x2 in theupper-left region.Determine thefactors of x2 and labelthe factors.

x2x

x

Determine the factors of x2 + 6x + 8:

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Problem 1

x2

Step 2: Place the units inthe lower-right region.

8

x

x

Determine the factors of x2 + 6x + 8:

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Problem 1

x2

8Step 3: Determine possible

factors (configurations) for the units.

x

x

Determine the factors of x2 + 6x + 8:

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Problem 1

x2

8Step 3: Determine possible

factors (configurations) for the units.

x

x

18

Determine the factors of x2 + 6x + 8:

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Problem 1

x2

8Step 4: Label the dimensions

and check the resulting products.

x

x

18

1

8

8x

x

Determine the factors of x2 + 6x + 8:

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Problem 1Determine the factors of x2 + 6x + 8:

x2

8

x

x

1

8

8x

x

The sum of the two products is 9x.

The sum of the two products should be 6x.

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Try another configuration.

Problem 1

x2

8Step 3: Determine possible

factors (configurations) for the units.

x

x

Determine the factors of x2 + 6x + 8:

42

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Problem 1Determine the factors of x2 + 6x + 8:

x2

8

Step 4: Label the dimensionsand check the resulting products.

42

x

x

2

4

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Problem 1Determine the factors of x2 + 6x + 8:

x2

8

x

x

2

4

4x

2x

The sum of the two products is 6x.

The sum of the two products should be 6x.

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This configuration works.

Problem 1Determine the factors of x2 + 6x + 8:

x2

8

x

x

2

4

4x

2x

Use the dimensions to identify the factors.

The factors of x2 + 6x + 8 are (x + 2)(x + 4).

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