Transcript Lesson 6-2

5-Minute Check on Chapter 2
Transparency 3-1
1. Evaluate 42 - |x - 7| if x = -3
2. Find 4.1  (-0.5)
Simplify each expression
4. (36d – 18) / (-9)
3. 8(-2c + 5) + 9c
5. A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops.
If one is chosen at random, what is the probability that it is
not green?
6.
Standardized Test Practice:
Which of the following is a true
statement
A
8/4 < 4/8
B
-4/8 < -8/4
C
-4/8 > -8/4
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D
-4/8 > 4/8
Lesson 9-2
Factoring Using the
Distributive Property
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Objectives
• Factor polynomials by using the Distributive
property
• Solve quadratic equations of the form ax2 + bx
=0
Vocabulary
• Factoring- to express the polynomial as the product
of monomials and polynomials
• Factoring by grouping– the use of the Distributive
Property to factor some polynomials having four or
more terms
Addition and Subtraction PoE
Properties of Equality (PoE) are based on the concept
that as long as you do the same thing to both sides
of an equation, then you have not changed anything.
• Addition PoE
– For any numbers a, b, and c, if a = b, then a + c = b + c
– You can add the same thing to both sides of an equation
without changing it.
• Subtraction PoE
– For any numbers a, b, and c, if a = b, then a - c = b - c
– You can subtract the same thing from both sides of an
equation without changing it.
Factoring by Grouping
• A polynomial can be factored by grouping if
all of the following situations exist:
– There are four or more terms
– Terms with common factors can be grouped
together
– The two common factors are identical or additive
inverses of each other
• In Symbols:
ax + bx + ay + by = x(a + b) + y(a + b)
= (x + y)(a + b)
Zero Product Property
• If the product of two factors is 0, then at least
one of the factors must be 0
• In Symbols:
If ab = 0 then either a = 0, b = 0 or both
Example 1a
Use the Distributive Property to factor
First, find the CGF of 15x and
.
.
Factor each number.
Circle the common prime factors.
GFC:
Write each term as the product of the GCF and its remaining factors.
Then use the Distributive Property to factor out the GCF.
Rewrite each term using
the GCF.
Simplify remaining factors.
Distributive Property
Answer: The completely factored form of
is
Example 1b
Use the Distributive Property to factor
.
Factor each number.
Circle the common prime factors.
GFC:
or
Rewrite each term using the GCF.
Distributive Property
Answer: The factored form of
is
Example 2
Factor
Group terms with
common factors.
Factor the GCF
from each grouping.
Answer:
Distributive Property
Example 3
Factor
Group terms with common factors.
Factor GCF from each grouping.
Answer:
Distributive Property
Example 4
Solve
Then check the solutions.
If
Property either
, then according to the Zero Product
or
Original equation
or
Set each factor equal to zero.
Solve each equation.
Answer: The solution set is
Example 5
Solve
Then check the solutions.
Write the equation so that it is of the form
Original equation
Subtract
from each side.
Factor the GCF of 4y and
which is 4y.
or
Zero Product Property
Solve each equation.
Answer: The solution set is
Check by substituting
0 and for y in the original equation.
Summary & Homework
• Summary:
– Find the greatest common factor and then use the
Distributive Property
– With four or more terms, trying factoring by
grouping. Factoring by Grouping: ax + bx + ay +
by = x(a +b) + y(a +b)= (a +b)(x +y)
– Factoring can be used to solve some problems.
• Homework:
– Pg. 484 16-36 even 48,52,58