Factoring Worksheet With Examples Page 16
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50Step 3
Arrange the 1-tiles
into a 1-by-6
rectangular array. This
time you can complete
the rectangle with the
x-tiles.
The rectangle has a
width of x + 1 and a
2
length of x + 6. Therefore, x
+ 7x + 6 = (x + 1)(x + 6).
3
2
ACTIVITY
Use algebra tiles to factor x
- 2x - 3.
Step 1
Model the polynomial
2
- 2x - 3.
x
2
Step 2
Place the x
-tile at the
corner of the product
mat. Arrange the
1-tiles into a 1-by-3
rectangular array as
shown.
Step 3
Place the x-tile as shown. Recall that you can add zero-pairs
without changing the value of the polynomial. In this case, add
a zero pair of x-tiles.
x
3
2
2
x
x x
x
x x x
x
1
x
1 1 1
1 1 1
zero pair
The rectangle has a width of x + 1 and a length of x - 3.
2
Therefore, x
- 2x - 3 = (x + 1)(x - 3).
A
NALYZE THE RESULTS
Use algebra tiles to factor each trinomial.
2
2
2
2
1. x
+ 4x + 3
2. x
+ 5x + 4
3. x
- x - 6
4. x
- 3x + 2
2
2
2
2
5. x
6. x
7. x
8. x
+ 7x + 12
- 4x + 4
- x - 2
- 6x + 8
9. Examine the dimensions of the rectangles in each factored model. How
does the sum of the dimensions compare to the coefficient of the x-
term? Explain how you could use this observation to factor trinomials.
433
Explore 8-3 Algebra Lab: Factoring Trinomials
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