Transcript 7.2 Notes - LHS Math Resources

MT7 Working With
Rationals
MT7 Working With Rationals
MT7 is going to be a longer topic than some of the other Algebra MT’s.
If you don’t know how to GCF (Greatest Common Factor), Diamond
Method (Factor an ABC Quadratic), or factor using Difference of Two
Squares, then you should not even try this topic entire you have passed
MT4.
After starting your 7.1 and 7.4 vocab assignment, you are going to start
this topic by reviewing how to factor (7.2). After taking 7.2 Quiz, you will
move to Reduce Rationals (7.3). Do the homework and take the 7.3
Quiz. I suggest skipping 7.51, 7.52, and 7.53 until the end and going
straight to 7.6 and 7.7. They are almost the same as 7.3 and the Quiz is
pretty easy. Do 7.5 last! It will take you a week to get through it, and
you’ll want to have that section fresh in your mind when you take the
EOT.
Lesson for 7.2: Review Factoring
There are three types of factoring you are going to have to master if you
are going to pass MT7. They are GCF, Diamond Method, and Difference
of Two Squares. We are going to look at a practice worksheet similar to
your homework and go over several problems from each type of
factoring.
If you have more questions after practicing your homework, be sure to
use online resources, friends, fellow students, and your LF to help you
gain understanding.
Lesson for 7.2: Review Factoring
This is an example of your
homework for 7.2, Factoring
Review. Let’s look at GCF
Factoring First.
Lesson for 7.2: Review Factoring
7
3
Make Parenthesis.
5
r2( 7 r3 -
3 )
Find a number that
goes into 35 and 15.
I choose 5.
5
1
Do it again…
10 x2( 5 x2 + 1 )
Now Divide
Why is it r3? What
happened to the r2?
5r2(7r3 – 3)
Now place your new
numbers in the ( )
Do they share a
variable (yes). r2 is
also shared!
Finish the ( )
10x2(5x2 – 1)
Notes: This is GCF Factoring (Greatest Common Factor). Find numbers or variables that go into
any of your numbers. Factoring means “Make Parenthesis”, so we should always start by making
parenthesis. When choosing from variables, all terms must have the variable and we always
choose the smallest exponent.
Lesson for 7.2: Review Factoring
Now GCF with three terms.
Lesson for 7.2: Review Factoring
5
1
10
x2y3
5 (5 xy+1
+10)
Notice this problem did
not share a variable for
all three terms.
Therefore, the variables
are not changed.
5(5xy+x2y3+10)
The same process,
except now we have
3 terms..
Start with ( ). Find a
GCF. Divide by the GCF.
Put your numbers into
the ( ). Decide if they
share a variable. Finish
it off.
-6
-7
-3
2mn2(-6m3n -7n2 -3 )
The “m’s” lose 1, the
“n’s” lose 2.
Notice we have a choice
of pulling out a -2
instead. This would
change all the signs in
the ( )
2mn2(-6m3m – 7n2 – 3)
Notes: These are a little bit longer, but still easy to do. Just be precise!
Lesson for 7.2: Review Factoring
Difference of 2 Squares. (The
easiest factoring of all)
Lesson for 7.2: Review Factoring
3•3 xx and 7•7
( 3x + 7 )(3x - 7 )
First make two sets
of ( ) and put + and
– in each one.
Break down your
perfect squares.
Each ( ) gets to
share the numbers.
(
Again with the same
pattern…
8•8 and 3•3 vv
( 8 + 3v )(8 - 3v)
(3x+7)(3x-7)
Notes: This only work if both pairs of numbers are perfect squares. Here is a limited list of some
perfect squares: 1, 4, 9, 16, 25, 36… and x2, x4, x6, x8. I hope you get the idea.
Lesson for 7.2: Review Factoring
And last of all, Diamond Method
Lesson for 7.2: Review Factoring
A
B
C
( r + 7 )( r - 4 )
You must be an expert
at this by now!
Please pay attention to
the steps.
AC: 1 • -28
-28
7 -4
+3
(r+7)(r-4)
B: +3
Make a list (
1•28
2•14
4•7
A little different
-1
10
(5n - 1 )(n + 2 )
-10
10
-1
+9
5 goes into 10, 2 times
1 goes into -1, -1 times
Notes: You must have an ABC pattern to do Diamond Method. Watch Out! Diamond Method
when a>1 can be tricky (#8).