Advanced Algebra
Chapter 6 “Polynomials and Polynomial Functions”
Section
Topic
6.1
Operations of Polynomials
Worksheet #1
6.1
Multiplying Monomials
Worksheet #2
6.1
Dividing Monomials/Polynomials
Worksheet #3
6.2
Dividing Polynomials using Long
Division
P. 345: 8-11all, 29, 30
6.2
Dividing Polynomials using Synthetic
Division
QUIZ (6.1-6.2)
Assignment
P. 345: 20-25all, 43,50,51,52
TBD
Factor
Factoring Trinomials
Worksheet #7
Factor
Factoring Binomials/Grouping
Worksheet #8
TASK/N-Spire
6.5
TBD
Solving Polynomial Equations
Worksheet #10
REVIEW
Review Packet
REVIEW
TBD
CHAPTER 6 TEST
Extra copies of the worksheets can be found on my website!!!
Advanced Algebra
6.1 Polynomial and Polynomial Functions
Day 1
Learning Target – Students will be able to add/subtract/multiply monomials involving powers.
Variable –
Coefficient –
Term –
Like Terms –
Expression –
Monomial –
Constant –
Degree of monomial –
Simplify.
1.
4a 3b  11a 3b  a 3b 
2.
12 x5  2 x 4  11x5  2 x 4 
3.
5a 2b3  2a 3b3  6a 2b3 
Remember the exponent rules:
aman 
(a m ) n 
(ab)m 
Simplify.
1.
(r 3 s 2 )(r 4 s 4t ) 
2. (ab2c3 )(a 2bc) 
3. ( x3 )4 
4. ( y 2 )3 
5. ( xy )3 
6. (3xy 2 )2 
2
1 
7.  x  
4 
8. (2 x 2 y )3 
9. (3a3b)(5a 2b2 ) 
10. (2ab2 )(4a3b3c) 
11. (6 x 2 y 3 )2 ( xy 2 z )3 
Advanced Algebra
6.1 Polynomial and Polynomial Functions
Day 2
Learning Target - Students will be able to multiply/divide expressions involving powers.
Remember the exponent rules:
aman 
am

an
(a m ) n 
a0 
(ab)m 
an 
Steps to Solve:
Simplify.
(a3b3c5 )10 (ab 4 c2 ) 1
2.

b3 (a 2cd 2 )2
(3rs)2 ( s3t )2
1.

12s 2t 4
3
2
3

4
2

5
3.  
4.  
2
(2 x5 y 3 z ) 2  4 x 2 y 2 z 3 

5.
 
(3x 9 y 11 z 2 ) 2  xyz 1 
Advanced Algebra
6.2 Dividing Polynomial Functions
Day 1
Learning Target – Students will be able to divide Polynomials by a Monomial.
Polynomial  Monomial (1 term) – Do term by term.
Divide:
3.
25a 4
1.
5a 2
8 x 2 y 3  28 x3 y 2
2.
4 xy 2
3a 2b  6a 3b 2  18ab
3ab
4. (4 x5  6 x 4  12 x3  8 x 2 )(4 x 2 ) 1
Advanced Algebra
6.2 Dividing Polynomial Functions
Day 2
Learning Target – Students will be able to divide Polynomials using Long Division.
Polynomial  Polynomial – if you can factor and cancel, DO IT! Otherwise, do long division.
1. (9b  9b  10)  (3b  2)
2. (5m2  34m  7)(m  7)1
3. (n3  6n2  13n  20)  (4  n)
4. ( x6  5 x3  x  1)  ( x  3)
5.
x 4  2 x3  6 x 2  8 x  10
x2
Advanced Algebra
6.2 Dividing Polynomial Functions
Day 3
Learning Target – Students will be able to divide Polynomials using synthetic division.
Synthetic Division – shortcut for long division if you are dividing by (x-c)
Divide using long division:
1.
2 x3  7 x 2  8 x  16
x4
Now divide by synthetic division:
2.
2 x3  7 x 2  8 x  16
x4
3.
5 x3  x 2  7
x 1
4.
x3  13x 2  12 x  8
x  12
Remember – you can only use
synthetic division when you are
dividing by a binomial of
degree 1
Advanced Algebra
Factoring Polynomials
Day 1
Learning Target – Students will be able to factor Trinomials.
Factoring – to break up as small as possible (factor until you can factor no more)
Factoring polynomials: always pull out the GCF (greatest common factor) FIRST!
Factor:
1. 12 y  15 y
2
3. 24a 2b  18ab 2
2. 16m n  12mn
2
4. 2 x3 yz 3  7 xy 5 z 2  5x 2 y 3 z 4
Factor trinomials (still check for GCF first):
5. x 2  2 x  35
6. x 2  13 x  30
7. 2 x 2  11x  21
8. 6 x 2  19 x  10
9. 16 x 2  24 x  9
Combined:
10. 3 x3  18 x 2  48 x
2
11. 18 x 4  32 y 6
Factoring Steps
1. Check for GCF
2. Determine if the
remaining polynomial
factors and proceed
3. Check all new
factors to see if they
can continue to factor
Advanced Algebra
Factoring Polynomial
Day 2
Learning Target – Students will be able to factor all types of binomials.
Certain types of factoring have patterns. Please identify the pattern of each type.
Difference of Squares:
x 2  16
Perfect Square Trinomial:
x 2  10 x  25
Difference of cubes:
x3  8
Sum of cubes:
x3  27
1. 4 x 2  25
2. x 4  18 x 2  81
3. 64 x 3  1
4. 8 x 3  125
Advanced Algebra
Factoring Polynomial
Day 3
Learning Target – Students will be able to factor by grouping.
Factor by grouping: If there are 4 or more terms, you will need to factor by grouping (usually by 2’s).
Factor:
1. a 2  2ab  a  2b
2. a 2 x  b2 x  a 2 y  b 2 y
Factoring Steps
1. Check for GCF
2. Determine if the
remaining polynomial
factors and proceed
3. x 3  5 x 2  2 x  10
4. a 2  3ay  2ay 2  6 y 3
Review of all factoring:
5. 3 x 3  6 x 2  3 x  6
6. 27 x3  8 y 3
7. 6 x 2  5 x  4
8. 2 x 2  32
9. 2 x 6  12 x 3  16
10. 5 x 4 y 2  15 x3 y 3
3. Check all new
factors to see if they
can continue to factor
Advanced Algebra
6.5 Solving Polynomial Equations
Day 1
Learning Target – Students will be able to solve polynomial functions by factoring.
Solve the equations by factoring.
1. x 2  x  6  0
Steps
1. Get equation set =0
2. Factor - remember to GCF first
(if possible)
3. Set each factor =0 then solve
2. 3 x 2  17 x  6  0
3. x 2  7 x  10
4. x3  25 x  0
5. 3 x3  12 x 2  2 x  8