Transcript Factor and Solve Quadratic Equations Ms. Nong What is in this unit?  Graph the quadratic equations (QE)  Solve by taking SquareRoot & Squaring 

Factor and Solve
Quadratic Equations
Ms. Nong
What is in this unit?
 Graph the quadratic equations (QE)
 Solve by taking SquareRoot & Squaring
 Solve by using the Quadratic Formula
 Solve by Completing the Square
 Factor & Solve Trinomials (split the middle)
 Factor & Solve DOTS: difference of two square
 Factor GCF (greatest common factors)
 Factor by Grouping
Ch 5 Greatest Common Factor
The greatest common factor (GCF) of two or more
terms is the greatest whole number that divides evenly
into each number.
One way to find the GCF of two or more numbers is to
list all the factors of each number. The GCF is the
greatest factor that appears in all the lists.
Course 2
Ch 5
Greatest Common Factor
Example: Using a List to Find the GCF
Find the greatest common factor (GCF).
12, 36, 54
12: 1, 2, 3, 4, 6, 12
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
54: 1, 2, 3, 6, 9, 18, 27, 54
The GCF is 6.
Course 2
List all of the factors
of each number.
Circle the greatest
factor that is in all
the lists.
2-5Insert
Lesson
Title Factor
Here
Greatest
Common
Try This:
Find the greatest common factor (GCF).
14, 28, 63
14: 1, 2, 7, 14
28: 1, 2, 4, 7, 14, 28
63: 1, 3, 7, 9, 21, 63
The GCF is 7.
Course 2
List all of the factors of
each number.
Circle the greatest
factor that is in all
the lists.
2-5 Greatest Common Factor
Additional Example: Using Prime Factorization to
Find the GCF
Find the greatest common factor (GCF).
A. 40, 56
40 = 2 · 2 · 2 · 5
56 = 2 · 2 · 2 · 7
2 · 2 · 2 = 8
The GFC is 8.
Course 2
Write the prime factorization of
each number and circle the
common factors.
Multiply the common prime
factors.
Common Group
Factoring Out the Greatest
Common Factor
Factor out the greatest common factor.
6 p  q  r  p  q
Solution:
 p  q  6  r 
y4  y  3  4  y  3
4
y

3
y

   4
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Slide 6.1 - 7
Factoring Four Term
Polynomials
When……
When does it work? Always
When should I use it? For any polynomial
but especially when you have 4 or more
terms.
Steps
1. Put ( ) around first 2 terms and () around
last 2 terms
2. Factor out a common factor so what is
left in the binomials is the same
3. Continue factor the group in common.
Factoring by Grouping
Use when there are 4 Terms
6x3 – 9x2 + 4x - 6
3x2(2x – 3) + 2(2x – 3)
(2x – 3) ( 3x2 + 2)
Factoring by Grouping
Use when there are 4 Terms
x 3 + x2 + x + 1
x2( x + 1)
+ 1( x + 1)
(x + 1) ( x2 + 1)
Factoring by Grouping
Use when there are 4 Terms
x3 + 2x2 - x - 2
x2( x + 2)
- 1( x + 2)
(x + 2) ( x2 - 1)
(x + 2) ( x - 1)(x + 1)
Note:
 If you have (a
- 3) and the second group is (3 - a)
ex: 2(a – 3) + 5a(3 - a) =
 You can take out a negative and switch like this…
2(a - 3) – 5a(a - 3) =
I take out a “-1” and multiply it to 5
The final answer is (a
– 3)(2 – 5a)
Last note:
Always apply GCF whenever possible!
Use Factor by Grouping when you are asked
to factor 4 or more terms.
Please complete the assignment & check
your answers.
The end.