Factoring Worksheet With Examples Page 15
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50Algebra Lab
EXPLORE
8-3
Factoring Trinomials
You can use algebra tiles to factor trinomials. If a polynomial represents
the area of a rectangle formed by algebra tiles, then the rectangle’s length
and width are factors of the polynomial.
2
1
ACTIVITY
Use algebra tiles to factor x
+ 6x + 5.
Step 1
Model
2
+ 6x + 5.
x
2
Step 2
Place the x
-tile at the
corner of the product
mat. Arrange the 1-
tiles into a rectangular
array. Because 5 is
prime, the 5 tiles can
be arranged in a
rectangle in one way, a
1-by-5 rectangle.
Step 3
Complete the rectangle
5
x
with the x-tiles.
The rectangle has a
2
x
x x x x x
width of x + 1 and a
x
1
length of x + 5.
x
1 1 1 1 1
Therefore,
2
x
+ 6x + 5 =
(x + 1)(x + 5).
2
2
ACTIVITY
Use algebra tiles to factor x
+ 7x + 6.
Step 1
Model
2
+ 7x + 6.
x
2
Step 2
Place the x
-tile at the corner of the product mat. Arrange the
1-tiles into a rectangular array. Since 6 = 2 × 3, try a 2-by-3
rectangle. Try to complete the rectangle. Notice that there are
two extra x-tiles.
Animation
2
2
x
x
x x x x x
x
x
1 1 1
1 1 1
x
x
1 1 1
1 1 1
432
Chapter 8 Factoring
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