Algebra 1
Chapter 9
Vodcasting for Mastery Learning
Name ________________________
Due Date:__________________
CHECKLIST
_____ A. Watch Vodcast #1- 9.1 Add and Subtract Polynomials and take notes
_____ B. Complete homework: p. 557, 4-26 even, 30 & 38
_____ C. Watch Vodcast #2 – 9.2 Multiply Polynomials, day 1 and take notes
_____ D. Complete homework: p. 565, 3-14
_____ E. Watch Vodcast #3 – 9.2 Multiply Polynomials, day 2 and take notes .
_____ F. Complete homework: p. 566, 18-38 even, & 50
_____ G. Watch Vodcast #4 –9.3 Find Special Products of Polynomials and take notes
_____ H. Complete homework: p. 572, 4-8, 12-16, 24-34 even
_____ I. Complete Review worksheet over 9.1-9.3
_____ J. Quiz #1 over 9.1-9.3 (Teacher Initials _______)
_____ K. Watch Vodcast #5 – 9.4 Solve Polynomial Equations in Factored Form and take notes
_____ L. Complete homework: p. 578, 4-15, 29-37, 51 & 52
_____ M. Complete Worksheet 9.4 B
_____ N. Watch Vodcast#6 – 9.5 Factor x2 + bx + c, day 1 and take notes
_____ O. Complete homework: p. 586, 3 - 17
_____ P. Watch Vodcast #7 – 9.5 Factor x2 + bx + c, day 2 and take notes
_____ Q. Complete homework: p. 586, 20-38 & 42
_____ R. Quiz #2 over 9.4-9.5 (Teacher Initials _______)
_____ S. Watch Vodcast #8 -- 9.6 Factor ax2 + bx + c, day 1 and take notes
_____ T. Complete homework: p. 596, 4-22 even
_____ U. Watch Vodcast #9 -- 9.6 Factor ax2 + bx + c, day 2 and take notes
_____ V. Complete homework: p. 597, 24-36 even
_____ W. Watch Vodcast #10 – 9.7 Factor Special Products and take notes
_____ X. Complete homework: p. 603, 4-36 even
_____ Y. Complete homework: Review worksheet of 9.4-9.7
_____ Z. Review Chapter 9, p. 616, 4-56 even and p. 621 # 32
_____ AA. Test over chapter 9 Polynomials and Factoring (Teacher Initials _______)
Chapter 9 Notes and Homework
9.1 Adding and Subtracting Polynomials
Objective: You will be able to add and subtract polynomials expressions.
Warm-up:
Simplify each expression
a) 5x + 4(2x + 7)
b) 9x - 6(x + 2) + 3
Vocabulary
Monomial-a one term expression
Examples: 10,
5x3, -45xy5z3
Polynomial -- sum of monomials
Examples: 2x3 + 4x2 - 9x -12
List the monomials in the example above:
*** A monomial or a polynomial must have whole number exponents of variables and it
cannot have variables in the denominator.
Standard Form of a polynomial-Polynomials should be written with the exponents going in decreasing order.
Degree of the polynomial-the highest exponent in the polynomial
Lead Coefficient of the polynomial-the coefficient of the first term when written in standard form
EXAMPLE FROM NOTES:
Write 3b3 -4b4 + b2 in standard form. Then identify the degree and the leading
coefficient of the polynomial.
Adding polynomials
You can only combine terms with similar variables and exponents.
You can align the polynomials vertically or horizontally.
Find the sum. Do #1 vertically & #2 horizontally, just to see which method you like the
best!!!
1. (2x3 -5x2 + x) + (2x2 + x3 - 1)
2. (3x2 + x - 6) + (x2 + 4x + 10)
Subtracting Polynomials
When subtracting polynomials, distribute the negative sign to all the terms inside the
parentheses and then add!
1. (4y2 + 5) - (-2y2 + 2y -4)
2. (6x5 - 3x2 + 4x +12) - (3x5 - x2 + 9)
Story Problem:
During the period 1999-2005, the number of hours an individual person watched
broadcast television B and cable and satellite television C can be modeled by
B = 2.8t2 - 35t + 879
C = -5t2 + 80t + 712
where t is the number of years since 1999.
About how many hours did people watch television in 2002?
9.1 Homework: p. 557, 4-26 even, 30 & 38
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9.1 Homework Continued
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9.2 Multiplying Polynomials, Day 1
Objective: You will be able to multiply monomials and polynomials as well as two
binomials using a table.
Warm-up:
Simplify each expression product.
1. -2(9a - b)
2. r2s rs3



Multiplying a Monomial and a Polynomial
Use the __________________ property to multiply to each term.
Multiply the coefficients together.
__________ the exponents.
1) 2x3(x3 + 3x2 - 2x + 5)
2) -x (2x3 - x2 + 4x - 3)
Multiplying two binomials...with a table
3 Steps:
1. Change any subtraction to addition.
2. Make a table of products.
3. Simplify the resulting polynomial.
Example 1: (x + 4)(2x - 1)
Example 2: (x - 4)(3x + 2)
Example 3: (4b - 5)( b - 1)
9.2 Homework: p. 565, 3-14
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9.2 Homework: p. 565, 3-14
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9.2 Multiplying Polynomials, Day 2
Multiplying Polynomials
Distribute each term of the binomial to each term of the polynomial.
Again, make sure to ___________ the exponents.
Combine like terms (Do NOT ________ the exponents when combining like
terms).
Write answers in standard form.
Examples:
1) (b2 + 6b - 7)(3b - 4)
2) (3x - 1)(2x3 - x - 2)
FOIL
Use FOIL to multiply 2 BINOMIALS.
F-------First
O-----Outside
I--------Inside
L--------Last
Example: (2x + 3)(4x + 1) = ____ + ____ + ____ + ____
1. (2r - 1)(5r + 3)
2. (s + 4)(s2 + 6s - 5)
Why can we use the FOIL process on the first example above but not on the second?
1. (3x - 2) (x + 9)
5)
2. (v + 3) (2v + 1)
3. (4n -1) (n +
Story Problem:
Dani has moved into her new house and has a lot of leftover moving boxes that she
wants to give away. She advertises her boxes online by giving the following dimensions:
Side 1: x + 3 inches
Side 2: 3x - 2 inches
Side 3: 16 inches
Find an equation to represent the volume of the box.
What is the volume of each box if x = 3.
9.2 Homework: p. 566, 18-38 even, & 50
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9.3 Special Products of Polynomials
Objective: You will be able to use special product patterns to multiply polynomials.
Warm-up:
Find the product of each by using the FOIL process.
1) (x + 6)(x + 6)
2) (5x - 3)(5x - 3)
Square of a Binomial Pattern:
(a + b)2 = a2 + 2ab + b2
EX: (x + 4)2 = ____ + ____ + ____
(a - b)2 = a2 - 2ab + b2
EX: (x - 7)2 = _____ - _____ + _____
Examples:
(x + 4)2 =
(x - 2)2 =
Find the product.
1. (x - 2)2
2. (m + 3)2
3. (7x + 2)2
4. (3x - 5)2
Sum and Difference Pattern
(a + b)(a - b) = a2 - b2
Ex: (x - 4)(x + 4) = x2 - 16
Why does this work?
Use FOIL to discover why...
1. (m + 9)(m - 9)
2. (x + 2)(x - 2)
3. (4n + 3)(4n - 3)
4. (3x - 7)(3x + 7)
Identify which special product pattern is used to help simplify each expression...
OR....you can simply FOIL the binomials!!
Examples:
1. (b + 7)2
2. (f + 1)(f - 1)
3. (2x - 1)2
9.3 Homework: p. 572, 4-8, 12-16, 24-34 even
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Review (9.1 – 9.3)
Find the sum or difference.
1.) (3m3 + 2m + 1) + (4m2 – 3m + 1)
2.) (-4y2 + y + 5) + (4 – 3y – y2)
3.) (-4c + c3 + 8) + (c2 – 5c – 3)
4.) (-3z + 6) – (4z2 – 7z – 8)
5.) (14x4 – 3x2 + 2) – (3x3 + 4x2 + 5)
6.) (5 – x4 – 2x3) – (-6x2 + 5x + 5)
7.) (10a2b2 – 7a2b) + (-4a3b2 + 5a2b2 – 3a2b + 5)
8.) (6m2n – 5mn2 – 8n + 2m) – (6n2m + 3m2n)
Find the product.
9.) -8y3(2y4 – 5y2 + 3)
10.) (b + 3)(3b2 – 2b + 1)
11.) (2y + 3)(y – 5)
12.) 4d2(-2d3 + 5d2 – 6d + 2)
13.) (6a – 3)(4a – 1)
14.) (n + 1)(n2 + 4n + 5)
Find the product of the square of the binomial.
15.) (x – 9)2
16.) (m + 11)2
18.) (2x + y)2
19.) (3y – x)2
17.) (5s + 2)2
20.) (10z – 3)2
Find the product of the sum and difference.
21.) (a – 9)(a + 9)
22.) (z – 20)(z + 20)
23.) (5r + 1)(5r – 1)
24.) (4 – w)(4 + w)
26.) (6m + 10)(6m – 10)
25.) (5 – 2y)(5 + 2y)
9.4 Solving Polynomial Equations
Objective: You will be able to solve polynomial equations when they are in factored
form
Zero-Product Property
Let a and b be real numbers.
If a  b = 0, then either a = 0 or b = 0
**This can be used to solve an equation when one side is zero and the other is the
product
of two or more polynomial factors.
EXAMPLE:
Solve (x -4)(x + 7) = 0.
Set each binomial equal to zero:
x-4=0
or
x+7=0
AND solve for x:
The answers of these equations are called solutions, zeroes or roots.
Solve:
1. (2x - 5) (x + 3) = 0
2. 12x(x - 7) = 0
If the polynomial is not in factored form, you have to get it in factored form.
Factor out the greatest common factor.
Then solve.
1. 3x2 + 18x = 0
2. 3s2 - 9s = 0
3. 4x2 = 2x
Vertical Motion Model:
h = -16t2+ vt + s
h=final height
t=time in seconds v=initial velocity(speed)
s=initial height
A dolphin jumped out of the water with an initial velocity of 32 feet per second. After
how many seconds did the dolphin re-enter the water?
A startled armadillo jumps straight into the air with an initial vertical velocity of 14
feet per second. After how many seconds does it land on the ground?
9.4 Homework: p. 578, 4-15, 29-37, 51 & 52
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9.5 Factor x2 + bx + c
Objective: You will be able to factor trinomials of the forms x2 + bx + c
Warm-up:
Find the product of (x + 4)(x + 3)
Factoring x2 + bx +c
x2 + bx + c = (x + p)(x + q)
provided that pq=c and p+q=b
When factoring a trinomial, first look at the signs you are working with:
x2 + 5x + 6
(x + 3)(x + 2)
EXAMPLES:
1. x2 - 4x + 3
x2 - x - 6
(x + 2)(x - 3)
x2 + x - 6
(x + 3)(x - 2)
x2 - 5x + 6
(x - 3)(x - 2)
2. t2 - 8t + 12
3. m2 + m - 20
4. w2 + 6w - 16
5. x2 - 2x - 24
6. x2 - 7x - 8
7. x2 + 8x - 20
8. x2 - 9x + 18
Quick Review...
To factor, follow these patterns:
1. x2 + bx + c = (x p)(x q)
2. x2 + bx - c = (x
p)(x
q)
3. x2 - bx + c = (x
p)(x
q)
4. x2 - bx - c = (x
p)(x
q)
Remember that pq=c and p+q=b
9.5 Homework: p. 586, 3 – 17
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9.5 Factor and Solve x2 + bx + c
Objective: You will be able to factor and solve polynomial equations.
Warm-up
Factor each trinomial below:
x2 - 6x - 16
x2 - 8x + 16
x2 + 10x + 16
Where we were…
Where we are going…
9.4: (x - 5)(x + 4)= 0  x = 5 or x = -4
(zero product property)
9.5, day 2: x2 - x - 20 = 0
(x - 5)(x + 4) = 0
x = 5 or x = -4
9.5, day 1: x2 - x - 20  (x - 5)(x + 4)
(Factoring trinomials)
Solve the equations.
1. z2 + 2z - 24 = 0
3. x2 + 7x = 18
2. x2 + 12x + 27 = 0
4. s2 – 12s = 13
Find the zeros of the polynomial function.
1. h(x) = -x2 + 5x + 24
2. g(x) = x2 + 10x - 39
The bandage shown has an area of 16 square centimeters. Find the width w of the
bandage.
9.5, day 2, Homework: p. 586, 20-38 & 42
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9.6 Factor ax2 + bx + c
Objective: You will be able to factor trinomials with a coefficient other than 1 for the
x2 term.
Warm-up:
Find the product of (3c + 3)(2c - 3)
So far, we have been factoring trinomials in the form x2 + bx + c
where the coefficient of x2 is 1. So our factors have all been the form (x ± __ )(x ± __
).
Now, we will be factoring trinomials that have a coefficient for x2 other than 1 (called
a) and we will have to factor it into two binomials.
Problem: 3k2 - 10 k + 8
Goal: (3k - 4 )(k - 2)
How do we factor a trinomial in the form ax2 + bx + c???
CHOP-CHOP METHOD:
Example: 3k2 – 10k + 8
Factor:
1. 2x2 - 7x + 3
2. - y2 + 2y + 8
3. 16m2 + 15m – 1
4. -3x2 - 13x – 4
5. 15a2 - 2a – 8
6. 5d2 - 18d – 8
9.6, day 1 Homework: p. 596, 4-22 even
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9.6, day 2 Solve ax2 + bx + c
Objective: You will be able to factor and solve trinomials with a coefficient other than
1 for the x2 term.
Warm-up:
Solve for c --> (3c + 1)(2c - 3) = 0
Factor and solve each polynomial using the zero product property:
1. 2x2 - 3x - 35 = 0
2. 7r2 + 2r = 5
3. -5m2 + 6m - 1 = 0
Hint for the lesson:
Make sure the trinomial is in standard form before trying to
factor it!
Example:
Like this8x2 - 4x + 2 = 0
Not this - 8x2 + 2 = 4x
9.6 day 2 Homework: p. 597, 24-36 even
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9.7 Factoring Special Products
Objective: You will be able to factor 2 special products.
Warm-up
Find the product of the following:
(m + 2)(m - 2)
(2y - 3)2
(s + 2t)(s - 2t)
The previous two examples can be summed up with our first special pattern:
Example:
4x2 - 9 = (2x + 3)(2x - 3)
Let's list the first 13 perfect squares to help out with factoring:
1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
Factor each difference of two squares polynomial.
1. y2 - 9
2. c2 - 36
3. 4y2 - 64
4. 169c2 – 16
Now factor each polynomial and solve for the given variable.
1. n2 - 81 = 0
2. 9y2 - 1 = 0
3. -9c2 = -16
4. 4z2 = 49
The second special pattern occurs when you factor perfect square trinomial equations
like the examples below. We usually just factor each polynomial and rewrite the
factors as a binomial squared.
Examples:
x2 + 6x + 9
and
x2 - 10x + 25
Factors:
(x + 3)(x + 3)
(x - 5)(x - 5)
2
Simplified:
(x + 3)
(x - 5)2
Factor each polynomial.
1. n2 - 12n + 36
2. w2 + 18w + 81
Factor and solve each polynomial.
1. x2 + 8x + 16 = 0
9.7 Homework: p. 603, 4-36 even
3. 4h2 - 32h + 64
2. m2 - 14m + 49 = 0
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Review Worksheet of 9.4-9,7
Write each equation in standard form (SF) on the first line. Factor the
equation on the second line (FF). On the third line, write the solutions (solns).
Write prime if the expression cannot be factored (on the second line).
1)
x2 = 4x – 3
SF________________
FF________________
solns ______________
2) x2 = 1
SF________________
FF________________
solns ______________
3) - 9 = - x2
SF _________________
FF__________________
solns ________________
4)
- 5x = - x2 – 4
SF________________
FF________________
solns ______________
5)
x2 + 9 = 10x
SF________________
FF________________
solns ______________
6)
1 = 49 x2
SF _________________
FF__________________
solns ________________
7)
x2 – 24 = 2x
SF________________
FF________________
solns ______________
8)
x2 – 6 – 13x = 24
SF________________
FF________________
solns ______________
9)
36 + x2 = 12x
SF _________________
FF__________________
solns ________________
10)
x2 = - 7x + 44
SF________________
FF________________
solns ______________
11) (x + 4)(x – 16) = - 12x
SF________________
FF________________
solns ______________
12) 2(3x + 4) = -x2
SF _________________
FF__________________
solns ________________
13)
25 - x2 = 0
SF________________
FF________________
solns ______________
14)
9x2 = 64
SF________________
FF________________
solns ______________
15) 10a2 – 19a = -6
SF _________________
FF__________________
solns ________________
Chapter 9 Review: p. 616, 4-56 even and p. 621 # 32
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Chapter 9 Test