Download 7.2 Common Monial Factoring/GCF

7-2 Factoring by GCF
Classwork: 01/23/17
Simplify.
1. 2(w + 1)
2. 3x(x2 – 4)
Find the GCF of each pair of monomials.
3. 4h2 and 6h
Holt McDougal Algebra 1
7-2 Factoring by GCF
Essential Questions
How do you factor polynomials by using
the greatest common factor?
Holt McDougal Algebra 1
7-2 Factoring by GCF
Writing Math
Aligning common factors can help you find the
greatest common factor of two or more terms.
Holt McDougal Algebra 1
7-2 Factoring by GCF
Example 1A: Factoring by Using the GCF
Factor each polynomial. Check your answer.
2x2 – 4
2x2 = 2 
xx
4=22
Find the GCF.
2
2x2 – (2  2)
The GCF of 2x2 and 4 is 2.
2(x2 – 2)
Check 2(x2 – 2)
2x2 – 4
Holt McDougal Algebra 1
The product is the original
polynomial.
7-2 Factoring by GCF
Example: Factoring by Using the GCF
8x3 – 4x2 – 16x
8x3 = 2  2  2 
x  x  x Find the GCF.
4x2 = 2  2 
xx
16x = 2  2  2  2  x
The GCF of 8x3, 4x2, and 16x is
4x.
22
x = 4x
4x(2x2 – x – 4)
Check 4x(2x2 – x – 4)
8x3 – 4x2 – 16x 
Holt McDougal Algebra 1
The product is the original
polynomials.
7-2 Factoring by GCF
Example: Factoring by Using the GCF
3x3 + 2x2 – 10
3x3 = 3
2x2 = 2 
 x  x  x Find the GCF.
xx
10 = 2  5
There are no common
factors other than 1.
3x3 + 2x2 – 10
Holt McDougal Algebra 1
The polynomial cannot be
factored further.
7-2 Factoring by GCF
Example: Factoring Out a Common Binomial Factor
A. 5(x + 2) + 3x(x + 2)
(x + 2)(5 + 3x)
Factor out (x + 2).
B. –2b(b2 + 1)+ (b2 + 1)
(b2 + 1)(–2b + 1)
Holt McDougal Algebra 1
Factor out (b2 + 1).
7-2 Factoring by GCF
Example: Factoring Out a Common Binomial Factor
Factor each expression.
C. 4z(z2 – 7) + 9(2z3 + 1)
There are no common
– 7) +
+ 1)
factors.
The expression cannot be factored.
Leave it the same way as the final answer
4z(z2
Holt McDougal Algebra 1
9(2z3
7-2 Factoring by GCF
You may be able to factor a polynomial by
grouping. When a polynomial has four terms,
you can make two groups and factor out the
GCF from each group.
Holt McDougal Algebra 1
7-2 Factoring by GCF
Example: Factoring by Grouping
6h4 – 4h3 + 12h – 8
(6h4 – 4h3) + (12h – 8) Group terms that have a common
number or variable as a factor.
2h3(3h – 2) + 4(3h – 2)
(3h – 2)(2h3 + 4)
Factor out (3h – 2).
Check (3h – 2)(2h3 + 4) =
Holt McDougal Algebra 1
6h4 – 4h3 + 12h – 8

7-2 Factoring by GCF
Lesson Quiz:
Factor each polynomial. (byb GCF)
1. 16x + 20x3
2. 4m4 – 12m2 + 8m
Factor each expression. (by grouping)
3. 7k(k – 3) + 4(k – 3)
4. 3y(2y + 3) – 5(2y + 3)
Holt McDougal Algebra 1