Download Concepts 1.1

Bell Work
4//2015
Find the factors.
1.
10
2.
16
3.
24
4.
26
Next Chapter
Chapter 8
Factoring Polynomials
Heading
5/24/2017
8.1 Factors and Greatest
Common Factors
Today we will find the prime
factorization and GCF of polynomials.
Students apply basic factoring techniques to
second-and simple third-degree polynomials.
These techniques include finding a common factor
for all terms in a polynomial, recognizing the
difference of two squares, and recognizing perfect
squares of binomials.
Notes
• Prime Number
= a whole number greater than 1 that has exactly two
whole numbers as factors, itself and 1.
• 2, 3, 5, 7, 11, …
• Prime Factorization
= All of the prime factors of a number.
• Hockey Stick Method
1. Write an upside-down division sign.
2. Determine a prime-factor (2, 3, 5, 7, 11,…).
3. Write the factor in front of the division sign
and place the quotient below.
4. Repeat until complete.
5. Write the prime factorization (the hockey stick).
Notes
Now you try.
Write the prime factorization.
Ex.
Ex.
Ex.
- Upside Down
2 60
2 84Division- Upside
2 Down
90 Division
- Try 2, 3, 5,
11, … - Try 2, 33, 5,
2 30
2 7,42
457, 11, …
- Anything else?
- Anything
15
3 15
3 21
3 else?
- Draw Hockey Stick - Draw Hockey
5
5 Stick
7
PF  22 3 5
PF  22 3 7
PF  2 32 5
Notes
• Greatest Common Factor (GCF)
= the highest factor of two or more numbers.
Find the GCF.
Ex.
24 and 30
Now you try.
Ex.
Ex.
18 and 45
20 and 36
2 24 30
3 12 15
4 5
3 18 45
3 6 15
2 5
2 20 36
2 10 18
5 9
GCF  6
GCF  9
GCF  4
Notes
Find the GCF.
Ex.
4 x 2 and 12 x
2
4x
12x
4
x x 2 3x
x 3
GCF  4x
Now you try.
Ex.
12 x 4 and 18 x3
3
4
18x
12x
6
x 3 2x 4 3x3
2x 3
GCF  6 x 3
Ex.
16 x 4 and 40 x 2
8 16x 4 40x 2
2
4
x 2 2x 5x
2x 2 5
GCF  8 x 2
Notes
Find the GCF.
Ex.
2 x3 , 4 x 2 , and 6 x
3
2
2x
4x 6x
2
x x3 2x 2 3x
x 2 2x 3
GCF  2x
Now you try.
Ex.
4 x 4 , 8 x3 , and 10 x 2
2 4x 4 8x 3 10x 2
2
4
3
2
5x
2x
4x
x
2x 2 4x 5
GCF  2 x 2
Summary
Write a summary about today’s lesson.
factorization just factor out
To find the prime ___________
prime factors in order (2, 3, __,
5 7, 11, …) using the
the ______
common
hockey stick method. To find the greatest ________
_______
factor just find the common factors and multiply them
together.
Ticket Out the Door
Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Find the GCF.
12 and 20
Today’s Homework
Rules for Homework
1. Pencil ONLY.
2. Must show all of your work.
• NO WORK = NO CREDIT
3. Must attempt EVERY problem.
4. Always check your answers.
Homework
8.1
Write the prime factorization.
1.
12
2.
28
3.
96
Find the GCF.
4. 15 and 20
7.
10.
8 x and 6
x3 , 5x 2 , and 7 x
5.
24 and 32
6.
45 and 75
8.
4 x 2 and 16 x
9.
24 x 4 and 40 x 2
11.
6 x 4 , 18 x3 , and 12 x