Concepts 1.1

1
Fridays Homework

• Any questions?
• Make sure the homework is 100 complete.
• Incomplete work will NOT be accepted.

2
Factoring Polynomials
6/8/2015
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.
3
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).
4
Notes
Now you try.
Write the prime factorization.
Ex.
Ex.
Ex.
- Upside Down Division
- Upside Down Division
- Try 2, 3, 5, 7, 11,
- Try 2, 3, 5, 7, 11,
- Anything else?
- Anything else?
- Draw Hockey Stick
- Draw Hockey Stick
5
Notes

• Greatest Common Factor (GCF)

the highest factor of two or more numbers.
Find the GCF.
Now you try.
Ex.
Ex.
Ex.
6
Notes

• Recall

• Distributive Property

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.
7
Notes

• Factoring by GCF

• Distributive Property BACKWARDS

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.
8
Notes
Factor.
Ex.
Ex.
What is the GCF?
What number goes in both?
What letter goes in both?
Now take out GCF.
What is left?
This takes too long.
Lets take off the training wheels.
9
Notes
Factor.
Ex.
Ex.
Ex.
What is the GCF?
What is the GCF?
What number goes in both?
What number goes in both?
What letter goes in both?
What letter goes in both?
Now you try.
Now take out GCF.
Now take out GCF.
Ex.
Ex.
Ex.
What is left?
What is left?
10
Notes
Factor.
Ex.
Ex.
Now you try.
Ex.
Ex.
11
Notes
Factor.
Ex.
Ex.
Ex.
Now you try.
Ex.
Ex.
Ex.
12
Summary
The first option to factoring is to take out
the _____. Find out which ________ and/or which
________ goes into every term in the parenthesis.
Once you find the GCF then take it ____. Last
keep inside the ___________ whatever is left-over.
GCF
number
variable
out
parenthesis
13
Todays Homework
Rules for Homework

• Pencil ONLY.
• Must show all of your work.
• NO WORK NO CREDIT
• Must attempt EVERY problem.
• Always check your answers.

14
Homework
Factor.
15
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.