Download 8-2A Factoring Using the Distributive Property

8-2A Factoring Using the
Distributive Property
I. Recognizing the GCF
PRACTICE
Remember, the GCF (greatest common factor) means finding
the greatest number that can “go into” two or more numbers.
Identify the GCF of each polynomial.
1. 5x, 30y
a2
5
4.
2. a5b, a2
8bc2,
24bc
8bc
3. 14gh, 18h
2h
5. 12ax3, 20bx2
4x2
6. 18x2, –30x4y
6x2
7. 24c2, 48cd
8. 28de2, 56d2e
9. 12a, 36a2, 8ab
24c
14de
4a
II. Factoring Simple Binomials
In Chapter 7, we learned how to multiply a monomial by a
binomial. Factoring is the reverse of multiplying. To factor
means to break down an expression into a product of two or more
expressions called factorizations.
Compare:
Factoring
Multiplying
Ex 1. 4a(3a + 4) = 12a2 + 16a
12a2 + 16a = 4a(3a + 4)
The goal is to pull out what the terms have in common. In other
words, factor out their GCF.
GCF (What’s left)
Note: when asked to factor, it is implied that you must factor
completely (always factor out as much as possible)
Ex 1. Factor each polynomial.
5x + 30y
GCF (What’s left)
5( x + 6y )
GCF
II. Factoring Simple Binomials
Factoring is the reverse of multiplying.
Pull Out What They Have In Common
Ex 2. Factor:
9x2 + 36x
9x( x + 4 )
GCF
II: Factoring Simple Binomials
Factoring is the reverse of multiplying.
Pull Out What They Have In Common
14gh + 18h
Ex, 3: Factor:
2h( 7g + 9 )
GCF
III. Larger Expressions
Factoring is the reverse of multiplying.
Pull Out What They Have In Common
4r2 + 8rs + 28r
Ex. 4 Factor :
4r( r + 2s + 7 )
Ex. 6: Factor: 8bc2
– 24bc
Note: Watch your signs!
8bc( c – 3 )
IV. PRACTICE
Factoring is the reverse of multiplying.
Pull Out What They Have In Common
1. 5x + 30y
2. 14gh – 18h
3. a5b – a
5(x + 6y)
2h(7g – 9)
a(a4b – 1)
4. 12ax3 + 20bx2 + 32cx 4x(3ax2 + 5bx + 8c)