Factorizing Algebraic Expressions Worksheet Page 8
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Example
Factorize 6x
12
x
2
2
1: Multiply the first term 6x
by
72x
2
the last term ( 12)
( 9x)(8x) = 72x
9x + 8x = x
2
2: Find factors of
72x
which
add to
x.
3: Return to the original ex-
pression and replace
x with
2
6x
12
x
9x + 8x.
2
= 6x
9x + 8x
12
2
4: Factorize (6x
9x) and (8x
= 3x(2x
3) + 4(2x
3)
12).
= (2x
3)(3x + 4)
5: One common factor is (2x
3). The other factor, (3x + 4),
is found by dividing each term
by (2x
3).
(3x + 4)(2x
3)
6: Verify the factorization by ex-
= 3x(2x
3) + 4(2x
3)
pansion
2
= 6x
9x + 8x
12
2
= 6x
12
x
2
Example 3 : Factorize 4x
+ 21x + 5.
2
2
1. Multiply first and last terms: 4x
× 5 = 20x
2
2
2. Find factors of 20x
which add to 21x and multiply to give 20x
. These are
20x and x.
3. Replace 21x in the original expression with 20x + x:
2
2
4x
+ 21x + 5 = 4x
+ 20x + x + 5
4. Factorize the first two terms and the last two terms
2
4x
+ 20x + x + 5 = 4x(x + 5) + (x + 5)
Page 8
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