Algebra II Notes Packet – Unit 3
Review of Properties of Exponents, Operations with Polynomials, Factoring
Name: ___________________________________________ Pd: _______
Section/ Topic
SOL
Review of Properties of
Exponents
Operations with Polynomials
5-4/
AII.1d
Quiz on Review of Properties of
Exponents, Operations with
Polynomials
Review of Factoring
Test on Algebra I Review
Homework
Line Up Dominoes
Polynomials SelfTest pages 5-6
Study pages 2-6
More Factoring
Practice – page 9
Test Review –
pages 10-11
Date due:
Grade:
Algebra II Notes – Review of Properties of Exponents
Multiplying Monomials Review: ______________Coefficients, ________ Powers!
Example 1:
Simplify:  2ab2  4a 3b3c 
Dividing Monomials Review: _______________Coefficients, __________ Powers!
3 x11
Example 2: Simplify:
27 x 8
Raising Monomials to a Power: __________________Multiplication
Example 3: Simplify:  6a 3b2 
4
Remember the Power of being Positive!
a  n  _______________
Example 4: Rewrite with positive powers:
a) 3x
b) 2 y
4
c) 7x y
7
3
8
4
d)  x 
2
Raising anything to the power of zero is quick and easy: a 0  _______________
Example 5:
 37 x 9 y 


  64 x 3 4 y 3 


0
Now try these...
1.
 4x y 
2
3
 3x 9 y 
2.  3 3 
 6x y 
2
1
 3a 
3.  2 
b 
3
Line up Dominoes: Algebra
Begin
x x 
8x y
1
x3 y 5
12 x

3 x 3 y 2
y4
x4
4x2
5 y3
(3xy )2

4
z
1y 3 z 2
5x4
 x2 
 2 
y 
4
7
2
5
27x
3
6
x8

3
x
4x 4
y2
14 x 1 y 3

5
21x
 2 x3  6 x 1 
 4  7  
 3 y  5 y 
x11
(3x 2 )3 
(4 xy 2 )(2 x 4 y) 
10
3x9 y 6
 80 x 6 y 7 
 3 8  
 5x y 
12x3 y 5
x 2 y 3

5 2
x y
(4 x)(5 y 4 )

(3xy 2 )(2 x9 )
 z4 
 2 2
 9x y 
2
0
x5
(3x2 )(4 y3 )( x5 y 2 ) 
2x4
3 y3
4 xyz 2

5 2
20 x y
1
END!
2x
End!
Line up Dominoes:
Each Domino is made up of 2 parts, answer on left side and expression on right side.
1.
2.
3.
4.
5.
Simplify each expression on a separate sheet of paper. (found on the left side of each domino)
Cut out all 15 Dominoes.
Start with the “Begin” Domino and connect the expression on the right side with the answer domino.
Each expression should match an answer on the right side of another domino.
In a line, tape together all 15 Dominoes with the “End” being last.
Example:
Begin
4x  7 x 
4x2

2x
11x
3
Operations with Polynomials...
Examples of polynomials:
3x  2 y  6 xy 3
4 x2  2 y
5xy 2
Review of Adding/Subtracting Polynomials: Add _________________ only!!!
Example 1: Add:
 4 x
Example 2: Subtract:
3
 3x  10 x 2   8 x 2  2 x  x 3  x 4 
2x
2
 3xy  5 y 2    4 x 2  3xy  2 y 2 
Example 3: What is the perimeter of the triangle shown in the drawing?
6x
x+7
4x + 7
Multiplying Using Distributive Property:
Example 4:
Example 3: 9a 2  3a  7b3 
 4 x  37 x  9
Example 5:
3 y  2
2
Quiz next block
on monomials
and polynomials!
Example 6:  x  12   2 x  10 x  4 
2
4
5
6
Warm-up and Review for Quiz: Polynomials Practice – online on Ms. Lawrence’s website
Notes - Review of Factoring
Factoring Flow Chart:
Factor out
a GCF
Example:
3
2
12 x  6 x y  15x 2  _____________
How
many
terms?
Two:
Three:
Difference of
Two Squares
a 2  b2  __________
“Berry Method”
Example:
2
x  3x  10  ____________
Four:
Factor
by
Grouping
Sum of Two
Cubes Formula (SOAP)
a 3  b3   a  b   a 2  ab  b 2 
3x 2  15xy  4 xy  20 y 2 
_________________
________________
Difference of
Two Cubes Formula (SOAP)
a 3  b3   a  b  a 2  ab  b 2


7
Factoring Examples:
1. 16m 2n  12mn 2
Trinomial Factoring:
1.
2.
3.
4.
5.
2. 3a 2  3b2  a 2 y  b2 y
ax 2  bx  c
“Berry Method”:
Write down two sets of parenthesis – put ax as first term in both ( )
Multiply first coefficient by the last. (ac)
Find factors of #2 (ac) that add up to the middle term (b)
Write the factors in the parenthesis.
Look at both parenthesis. Factor out a gcf out of one set of ( ).
3. 4 x 2  7 x  3
4. 7 x 2  16 x  4
5. The area of a rectangle is represented by the expression 2x2 + 5x + 2.
Which is an equivalent expression for this area?
Sum/Difference of Cubes - “SOAP” Formula:
a 3  b3   a  b  a 2  ab  b 2
a 3  b3
Examples:
6. x 3  125

 a  b a
2
 ab  b 2
7. 8  27 y 3
8


Online practice: Practice Using Factoring Formulas Self-Test – link found on Ms. Lawrence’s
website under the “Algebra 2 Links” tab.
Classwork: Mixed Factoring Practice
Grade: _____ out of 5
1.
6r 2  10r  24 
2.
4 x2  4 x  1 
3.
x2  3x  10 
4.
45x2  320 x  35 
5.
x2  4 xy  4 y 2 
6.
6 x2  7 x  10 
100a2  50c2 
8.
6 x2  5x  21 
7.
Homework: More Factoring Practice
2
1. 5 p  22 p  8
2. x 3 125
3. 32  18r  r 2


4. a b  5ab  6


5. 8a  27
2 2
6. 125  m 3
3

7. 20m 2  13mn  2n 2



10. 24a  375b
3

3
9

3
9. 54 y  2
8. 15s2 16st  4t 2
Test Review:
Simplify.
3x2 
3
7 4
1. f f
2.
2
3 2 4 
c f
cd
3 
4. 5
3.
5. 4 x 2 y  9 xy 2   3x 2 y  6 xy 2 
2y4xy3
6.
7. The length of a rectangular classroom floor is 19 feet less than twice the width.
w
2w - 19
What expression represents the perimeter of the classroom floor?
What expression represents the area of the classroom floor?
Factor.
8. 200x2 – 50
9. s3 + 512
10. 10r2 + 14rs – 12s2
10
Factor.
11.
3a3b  12a2b  63ab 
13.
x2 y  xy3 
14.
x2 y 2  4 xy  3 
15.
y 2  35  2 y 
16.
25a2  4 
12.
2a2  28a  98 
17. If the area of a rectangle can be represented by x2 - 25, which could represent its length
and width?
Don’t forget to
study for your
test!
11