Polynomials 6.12 Factoring.notebook
Factoring Using Distributive Property
Polynomials
• I can factor polynomials using the Distributive Property.
TEKs
10.E ­ Factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two answer
Title Page
1. 1, 41; prime
2. 1, 11, 121; composite
3. 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90; composite
4. 1, 3, 5, 15, 191, 573, 955, 2865; composite
5. 2 · 2 · 2 · 3 · 5 · 5
6. 5 · 5 · 7
7. ­1 · 2 · 3 · 5 · 5
8. 2 · 2 · 2 · 2 · 2 · x · x
9. 2 · 3 · 3 · m · m · n
10. 7 · 7 · a · a · a · b · b
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Warm Up
49x
Practice 4ab
Answers
4
6a
7y
2mn
38 in.
170 in.
12­in. square
12
Maintain Your Skills
1. D
2. A
3. B
Homework Answers
Jan 21­4:51 PM
Factors vs.
Prime Factorization
Math Humor
Introduction
1
Polynomials 6.12 Factoring.notebook
________ Factoring using the Date
1. What are inverse operations?
Distributive Property
• Addition & Subtraction
2. What is simplest form of factored polynomial?
• completely factored
• GCF is 1
• relatively prime
• Multiplication & Division
2a(2a + 4)
• Squared & Square Root
factor
out
another
2
• Distributing & Factoring
Notes
3. How to factor a polynomial?
Notes
• Find GCF of coefficients
• Find GCF of each variable
4. What is factor by grouping?
• recognize binomials that are additive inverses
•
polynomial has 4 or more terms
• terms with common factors
grouped together
• change to the form a(c+d) + b(c+d)
•
use FOIL to check
These are
the same!
(y-7) + (7-y)
(y-7) + -1(y-7)
4(2+a) + b(2+a)
(4+b)(2+a)
Notes
Find a friend and tell them how you know a polynomial is in its simplest form.
Find a Friend
These are
the same!
Notes
Always feel like you're walking on ice...
feel like a 40 mph wind is blowing in your face?
Would You Rather?
2
Polynomials 6.12 Factoring.notebook
It's the
opposite of
distributive
property
Factoring
Binomials
Examples
1. Factor the polynomial, distribute to check
12a2 + 16a
4x ­ 2
factor out a 2
2(2x ­ 1)
simplest form ­ like reducing fractions
answer
Reminder
4a(3a + 4) Check by using distrib. method to multiply
Examples
2. Factor the polynomial, distribute to check
3. Factor the polynomial by grouping
4ab + 8b + 3a + 6
18cd2 + 12c2d + 9cd
a(c+d) + b(c+d)
answer
answer
3cd(6d + 4c + 3)
Examples
(4ab +3a)(8b+6)
a(4b + 3) + 2(4b+3)
(a+2)(4b+3)
Examples
Application
4. Factor using grouping
Coach Jones is scheduling the league baseball games. To find the number of games needed, he can use this equation. 35x ­ 5xy + 3y ­21
1
1
2 ­ n
g= n
2
2
g = # of games
n = # of teams
a. Write the equation in factored form.
b. How many games are needed for 5 teams to play each other exactly 4 times?
d) + b(c+d)
answer
answer
Examples
(y – 7)(­5x + 3)
a. g = 1/2n(n­1)
b. 1/2(52) ­ 1/2(5) = 10
10 x 4 = 40 games
Application
3
Polynomials 6.12 Factoring.notebook
Practice
Factoring
Worksheet
Activity
Homework
Closing Questions
Is there more than one way to group polynomials when factoring? (yes)
How can you check answers after factoring? FOIL
Closing Questions
4