Download 9-2 factoring using the distributive property

9­2 factoring using the distributive property
Warm up: p. 479 #72­86 even
Title: Factoring Using the Distributive Property
February 19, 2013
Factoring by using the distributive property
• You can reverse what we learned in chapter 8 to express a polynomial as the product of a monomial factor and a polynomial factor.
Example: Factored form:
EQ: How do we factor polynomials by using the distributive property? How do we solve quadratic equations of the form ax + bx + c?
Feb 19­11:53 AM
Feb 19­11:53 AM
Notes cont.
• Factoring involves finding the GCF
Example:
• Now you write each term as the product of the GCF (divide it out)
Example:
• This will give you the factored form of:
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
Feb 19­11:53 AM
Feb 19­11:53 AM
1
9­2 factoring using the distributive property
February 19, 2013
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
Feb 19­11:53 AM
Feb 19­11:53 AM
Use the Distributive Property to factor each polynomial.
a.
Answer
: b.
Answer
: Example 2­1b
Feb 19­11:53 AM
Feb 19­11:58 AM
2
9­2 factoring using the distributive property
February 19, 2013
Grouping to factor
• If a polynomial has four or more terms it helps to group the polynomial and then factor. This means you take and split the polynomial into pairs.
HINTS for grouping:
• There are four or more terms
• Terms with common factors should be grouped together.
• The two common factors are identical or additive inverses of each other.
Example:
Factor Answer
: Feb 19­11:53 AM
Feb 19­11:53 AM
The additive inverse property
• Recognizing the polynomial as additive inverses can be VERY helpful when factoring by grouping. Additive inverses are like (x­7) (7+x). You know they are additive inverses bc when you add them together the sum is 0. Parenthesis are identical except for signs! You need to pull out a negative in one of the outside numbers
• Example: Factor Group terms with common factors.
Parenthesis are identical except for signs! You need to pull out a negative in one of the outside numbers
= ­3a ﴾­5 + b﴿ + 4 ﴾b – 5﴿What is outside goes in one parenthesis and what is inside goes onto another.
Answer
: Distributive Property
Example 2­3a
Feb 19­11:53 AM
Feb 19­11:53 AM
3
9­2 factoring using the distributive property
February 19, 2013
Factor Factor Answer
: Answer
: Distributive Property
Example 2­3b
Feb 19­11:53 AM
Zero product property
• If the product of two factors is 0, then at least one of the two factors is 0.
Feb 19­11:53 AM
Feb 19­11:53 AM
Solve an equation in factored form
• Set up the two binomials so they are equal to zero and then solve for the variable.
Example:
Feb 19­11:53 AM
4
9­2 factoring using the distributive property
Solve
If
either
Check Substitute 2 and for x in the original equation. Then check the solutions. , then according to the Zero Product Property or Original equation
or
February 19, 2013
Set each factor equal to zero.
Solve each equation.
Answer: The solution set is
Example 2­4a
Feb 19­11:53 AM
Example 2­4a
Feb 19­11:53 AM
Solve and equation by factoring
Solve
Then check the solutions. • Write the equation so it is in the form of ab=0
• Then solve for x.
Example:
Answer: {3, –2}
Example 2­4b
Feb 19­11:53 AM
Feb 19­11:53 AM
5
9­2 factoring using the distributive property
Answer: The solution set is Check by substituting
0 and for y in the original equation.
Solve Then check the solutions. Write the equation so that it is of the form Original equation
Subtract or
February 19, 2013
from each side.
Factor the GCF of 4
y and
Zero Product Property
which is 4y. Solve each equation.
Example 2­5a
Feb 19­11:53 AM
Example 2­5a
Feb 19­11:53 AM
Practice/HW
Solve
• P. 484 #32­62 even
Answe
r:
Example 2­5b
Feb 19­11:53 AM
Feb 19­11:53 AM
6