Download Factoring using BFF

Factoring using BFF
Mastery Group 1
Greatest Common Factor
What is a factor?
Factors are the pieces that can be
multiplied to give you a final
product.
Example: The factors of 8 are
1,2,4,8. Multiplying matched pairs
of these numbers will give you 8
as an answer.
We also say that a number is a factor
of another number if that factor can
divide into the other number
without a remainder.
Example:
8 is a factor of 32 because 32÷8 = 4.
6 is not a factor of 32 because 32÷6 = 5 R2
What does it mean to factor an expression?
This means to break the expression into a product of two pieces.
A trip down memory lane…
We have used the distributive property with expressions.
4 x(5 x  6)
 4 x 5x  4 x 6
 20 x 2  24 x
The 4x multiplies to each term inside the
parentheses. The end result is that both the 5x
and the 6 now have 4x times as much.
Factoring using BFF
Factoring using BFF is to reverse a distributive property. We start with the answer, and
need to “pull out” (divide) a common factor from each term. This is the most basic
(and yet super important) kind of factoring, so we remember it by using BFF – Basic
Factor First. Doing this kind of factoring is going to be your “best friend forever” as you
move forward into more complicated factoring. It is the first step of EVERY complex
factoring problem!
Factoring with BFF
The main purpose of BFF is to take a problem that looks like ax + b, and
make it into a problem like c(dx + e).
We will use our skills with factoring to “un-distribute” these problems.
Factoring with BFF
Here is how this method works. You start with an expression like:
12 x 3  8 x
Break the terms of your expression down into pieces. A factor tree can be handy to start.
12 x 3  8 x
4 3
x x x
4 2 x
Now, you will notice that there are factors that appear in both the blue branches and
the red branches. These are what was once given to each term. Circle those factors.
I notice that I circled a 4 and an x in each tree. Multiply those together to get 4x. Now
we assemble our answer, which will be of the form _____(______+_______).
_____(______+_______)
4x
3x2
2
What both terms
had in common
What the first
term had left in
its tree.
What the second
term had left in
its tree.
Another example, another way
Another way to look at this is to ask some questions about an expression.
18 x 4  24 x3
1. What is the largest number that divides equally into both 18 and 24?
6
2. Look now at the x variable. What is the smallest exponent for that variable?
3, so x3
3. Put a 6x3 in front of parentheses. Divide each of the original terms by that
6x3, putting the answers in the parentheses.
18 x 4
 3x
6 x3
24 x3
 4
3
6x
6 x (3x  4)
3
More examples
9 x  27 x
2
9 1
x x
5
9 3 xxx x x
Special Note: When the first term is negative, you must
divide out a negative from all terms.
9 x 2 (1  3x3 )
20 x 6  13x
The biggest number that divides
into 20 and 13 is 1.
The smallest x term is just x. I will
be pulling out (dividing by) an 1x.
The first term is negative, so I am going to
take out a negative. This will change the plus
to a minus.
20 x 6
 20 x5
1x
13 x
 13
1x
1x(20 x5  13)
Your turn! Try to factor each one, then
click to check the result.
16 x3  8 x 2  8 x 2 (2 x  1)
10 x5  15 x8  5 x5 (2  3x3 )
4 x 2  8 x3  4 x 2 (1  2 x)
24 x2 y 4  15xy  3xy(8xy3  5)
Your task!
• Work together on worksheet 7.
• Plan how you will teach this to your
classmates tomorrow. Your plan should
include the following items:
– 3 examples to show. 1 to explain the steps, 1 to
show the steps again, and 1 for any special tricks.
– A short script for yourself.
– How to know if the group “gets it”.