Download Concepts 1.1

Friday’s Homework
1. Any questions?
2. Make sure the homework is 100% complete.
• Incomplete work will NOT be accepted.
Factoring Polynomials
5/23/2017
Factoring by GCF
Objective: factor polynomials by
taking out the GCF.
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
• Recall
• Distributive Property
a (b  c )
 ab  ac
a (b  c )
 ab  ac
When we distribute, all we are doing is multiplying
whatever is outside the parenthesis with what is inside.
Distribution changes a multiplication problem into
an addition or subtraction problem.
Notes
• Factoring by GCF
• Distributive Property BACKWARDS
ab  ac
 a b  c 
ab  ac
 a b  c 
When we factor, all we are doing is pulling out the
GCF of all terms inside the parenthesis.
Factoring changes an addition/subtraction
problem into a multiplication problem.
Notes
Factor.
Ex.
3x 2  6 x
2
 6x
3x
3
x x 2  2x
x 2
3x  x 22
 3x
This takes too long.
Lets take off the
training wheels.
Ex.
3x 2  6 x
GCF  3 x
 3x
3x  x  22
What is the GCF?
What number goes
in both?
What letter goes
in both?
Now take out GCF.
What is left?
Notes
Factor.
Ex.
8x 12
GCF  4
4422x
x  3
Now you try.
Ex.
12x  30
GCF  6
2xx  55
 62
Ex.
What is the
7 x 2GCF?
 9x
Ex.
What is5the
GCF?
x2 
20 x
What number
GCF goes
x
in both?
What number
GCF  goes
5x
in both?
What letter goes
in both?
What letter goes
in both?
Now take out GCF.
Ex.
What
4 xis3 left?
5x
Now take out GCF.
Ex.
What
4 x 2isleft?
28 x
 x 7x
7 x 99
GCF  x
 xx 4x
4 x2 55 
 55xx  x  44
GCF  4 x
 4x
4 x  xx77
Notes
Factor.
Ex.
Ex.
6 x 2  9 x  12
GCF  3
22
2x
 33 2 x 3x
3x44
2 x3  6 x 2  10 x
GCF  2 x

 2x
2 x xx223x
3x55

Now you try.
Ex.
Ex.
4 x3  8 x 2  9 x
GCF  x


 x 4x
4 x 8x
8 x 99
2
8 x 3  12 x 2  16 x
GCF  4 x


 4x
4 x 2x
2 x22 3x
3 x44
Notes
Factor.
Ex.
Ex.
8x  4
GCF  4
 4 2x
2 x 11
10x  14
GCF  2
 2 5x
5x 77
Ex.
6 x5  15 x 4  21x 2
GCF  3 x 2

 3x
3 x22 2x
2 x335x
5 x2 277
Now you try.
Ex.
Ex.
15 x  5
GCF  5
2


 5 33xx 2  1
9 x 15
GCF  3
 3 3x
3x 55
Ex.
10 x  20 x  45 x
GCF  5 x
5

3
4
22
2x
 55x
x 2 x 4x
4 x 99


Summary
The first option to factoring is to take out the
GCF Find out which ________
number and/or which
_____.
variable goes into every term in the parenthesis. Once
________
out Last keep inside
you find the GCF then take it ____.
parenthesis whatever is left-over.
the ___________
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
Factor.
1.
5 x  15
2.
6 x  10
3.
4 x2  7 x
4.
2 x2  6 x
5.
8x 2  12 x
6.
3x 2  6 x  6
7.
6 x 2  8 x  12
8.
7 x3  5 x 2  4 x
9.
4 x3  16 x 2  12 x
10.
4 x3  8 x 2  6 x
11.
6x  3
12.
16 x 2  8
13.
 3x  12
14.
 8 x 2  12 x
15.
2 x5  4 x3  5 x 2
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.
Factor.
4 x 2  12 x  8

 4 x 2  3x  2
