Factoring Trinomials NEXT. Problem 1 Product: x 2 + 6x + 8 Step 1: Place the x 2 model in the...
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Transcript of Factoring Trinomials NEXT. Problem 1 Product: x 2 + 6x + 8 Step 1: Place the x 2 model in the...
Factoring Trinomials
NEXT
Problem 1
Product: x2 + 6x + 8Step 1: Place the x2 model in the upper-left region.
NEXT
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.
NEXT
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.
NEXT
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:
NEXT
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:
NEXT
Problem 1
x2
Step 2: Place the units inthe lower-right region.
8
x
x
Determine the factors of x2 + 6x + 8:
NEXT
Problem 1
x2
8Step 3: Determine possible
factors (configurations) for the units.
x
x
Determine the factors of x2 + 6x + 8:
NEXT
Problem 1
x2
8Step 3: Determine possible
factors (configurations) for the units.
x
x
18
Determine the factors of x2 + 6x + 8:
NEXT
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:
NEXT
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.
NEXT
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
NEXT
Problem 1Determine the factors of x2 + 6x + 8:
x2
8
Step 4: Label the dimensionsand check the resulting products.
42
x
x
2
4
NEXT
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.
NEXT
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).
NEXT