Page 16 - iMath K to 12 Curriculum Series]

The following are examples of prime factors:

3, 17, x, 3x, x + 1, 3x - 1.

The following examples below show how to factor monomials:

Example 1:
4
List all possible factors of 20x :

3
2
4
Factors of 20x are 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 20, -20, x, x , x , x 4
3
3
2
2
(x)(20x ) (2x)(10x ) (4x )(5x )
2
2
2
4
2
(10)(2x ) (-x )(-20x ) (-4x )(-5x )
C
H Example 2:
A Find the factors of -6x .
5
P
T Rule for integers: (-)(+)
4
5
E Factors of -6: (1)(-6) ; (-1)(6) Factors of x : (x )(x)
2
3
R (3)(-2) ; (-3)(2) (x )(x )
1 Possible factors: (x )(-6x), (-x )(6x), (3x )(-2x), (-3x )(2x)
4
4
4
4
2
3
2
3
2
2
3
3
2 (x )(-6x ), (-x )(6x ), (3x )( -2x ), (-3x )(2x )
3 CONCEPT REVIEW
4 Find all possible factors of the following monomials. 2
2
6.
1. -11x
-3x
5 2. 17xy 7. 6x 2
2 2
6 3. 13x 8. 4x y
2
4. -y
3z
9.
7 5. 5x y 10. 7m
3 2
8
KEYNOTES
9 • Factoring is the counterpart of multiplying. To factor an expression is to
write an equivalent expression that is a product of two or more expressions.
• Any polynomial that cannot be written as the product of two other
polynomials, except 1 and -1, is said to be prime. A polynomial is said to be
factored completely when it has been written as a product consisting only
of prime factors.
4
iMath 8: K to 12 Curriculum Series