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Name:____________________________ Mr. Pistawka Date:______________________________ FMPC 10
Unit 3: Factors and Products Outline
3.1– Factors and Multiples of Whole Numbers • Watch Lesson Video & Complete Notes • Assignment: pg. 140-‐141, #3ace, 4ace, 6ace, 8ace, 15ac, 17
3.2– Perfect Squares, Perfect Cubes and Their Roots
• Watch Lesson Video & Complete Notes • Assignment: pg. 146,147, #4ace, 5ace, 7a, 8a, 10, 16, 17 • Quiz 3.1-‐3.2 (Moodle)
3.3– Common Factors of a Polynomial
• Watch Lesson Video & Complete Notes • Assignment: pg. 155,156, #4abc, 7ace, 8ace, 9ace, 10ace, 16ace, 21
3.5– Polynomials of the form x2 + bx + c • Watch Lesson Video & Complete Notes • Assignment: pg. 166,167, #4ac, 5ac, 11aceg, 12aceg, 21ace
3.6– Polynomials of the form ax2 + bx + c
• Watch Lesson Video & Complete Notes • Assignment: pg. 177,178, #6ace, 9ac, 12abc, 13ace, 15aceg, 19aceg • Quiz 3.3-‐3.6 (Moodle)
3.7– Multiplying Polynomials
• Watch Lesson Video & Complete Notes • Assignment: pg. 186, 187 #4ac, 6, 9ac, 12, 16, 19ace
3.8-‐ Factoring Special Polynomials
• Watch Lesson Video & Complete Notes • Assignment: pg. 194, 195 #4ace, 5, 8ace, 11ace, 15, 20
Review
• Practice Test via Moodle (Make corrections in your journal) • Review Assignment: Complete Attached Questions • ‘Hot Seat’ with Mr. Pistawka
o Once the above is completed you will schedule an in-‐class appointment to meet Mr. Pistawka on the ‘Hot Seat’ to show your learning evidence and discuss your understanding of the learning outcomes from the unit. If Mr.
Pistawka believes you have done quality work and have a strong understanding of the learning outcomes you will then be able to write your Unit Test. If Mr. Pistawka does not think your work is of high quality or you do not have a strong enough understanding you will be asked to complete some additional learning activities or improve your work you have already completed.
Write Unit Test • If you achieve greater than 60% on the unit test you can proceed to Unit 3 –
Factors and Products. If you get less than 60% on the unit test (don’t worry – be happy, life will go on) please see Mr. Pistawka for some extra support to help improve on your next attempt
Calendar – (This will be subject to change but it a rough outline) – Fill on as per Mr. Pistawka
1 goal I have for this unit is to: __________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________
Name:__________________ FMPC 10 Mr. Pistawka
3.1 Factors and Multiples of Whole Numbers Definitions: Prime Number: A prime number is any number that is only divisible by one and itself
ex.
Composite Number: Any number that is NOT a prime number or one that is divisible by
a number other and 1 or itself
ex.
Factor: One of two or more numbers that when multiplied together produce a given product
ex.
Prime Factor: Any factor that is a prime number
ex.
Greatest Common Factor (GCF): The largest # that both numbers are divisible by
ex.
Least Common Multiple: The first multiple that is the same for 2 #’s
ex.
Ex#1. Write the Prime Factorization for 4400
Method # 1 Method #2
Ex #2 Determine the GCF of 188 and 124
Ex #3 Determine the LCM of 18, 20, 30
Check your Understanding What are the dimensions of the smallest square that could be tiled using an 18-‐cm by 24-‐cm tile? Assume the tiles cannot be cut
3.2 Perfect Squares, Perfect Cubes and Their Roots
Any ________________________ that can be represented as the ________________ of a_________________ with a whole number side length is a perfect square. The _________________________________________________ of the square is the square root of the area of that square
Any ________________________ that can be represented as the ________________ of a _________________ with a whole number edge length is a perfect cube. The edge length is the _________________________________________________ of the volume of the cube
Ex#1. Determine the Square Root of 1024
Method # 1 – Prime Factors Method #2 -‐ Estimate
x x2 x3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Ex #2 Determine the Cube Root of 5832 Method # 1 – Prime Factors Method #2 -‐ Estimate Ex #3 A cube has a volume of 4096 cm3. Determine the area of one of its square faces.
3.3 Common Factors of a Polynomial Try this yourself
In Arithmetic In Algebra MULTIPLY factors to form a product
2 6 = _________
EXPAND an expression to form a product.
4 3 − 5𝑎 = ________________
FACTOR a number by writing it as a product of factors
12 = _____________
FACTOR a polynomial by writing is as a product of factors.
12 − 20𝑎 = _________________
We can say that these two operations are _________________________ of each other When we are asked to write a polynomial as a product of its factors, we simply factor the polynomial Ex#1 Use Algebra Tiles to Factor Polynomials *Recall Area of a Rectangle is L x W
a) 2x + 4
b) 3f + 9f2 c) 4 – 8b – 4b2 *We can always check our solutions when factoring, we simply expand our factors to see if it matches our original polynomial Ex#2 Use GCF to Factor Polynomials
a) 2x + 4 b) 3f + 9f2
c) 4 – 8b – 4b2 Ex#3 Factoring Polynomials w/ more than one Variable Factor: -‐10x3y – 5xy2 + 25x2y2
3.5/3.6 Polynomials of the form ax2+bx+c Ex#1 Factor. Check by Expanding 2x2 +14x+12 Steps: 1. Write out all Multiples of AxC (T-‐Chart) 2. Find out two multiples which add to B 3 Group 4. Factor out Common Factors 5. Re-‐Write as binomials Ex#2 Factor. Check by Expanding x2 + 11x + 18
Ex#3 Factor. Check by Expanding -‐24 – 5b + b2
Ex#4 Factor. Check by Expanding 2x2 + 13x + 6
Ex#5 Factor. Check by Expanding 2b2 + 9b -‐ 18 Ex#6 Factor. Check by Expanding 40y2 + y -‐ 6
3.7 Multiplying Polynomials Ex #1 Expand and Simplify (2x+6)(x2-‐3x-‐2) How to Check: 1. Set answer = to original expression 2. Plug in a value for the variable 3. See if they match Ex #2 Expand and Simplify (-‐4r2-‐4r+3)(2r2+3r-‐2)
Ex #3 Expand and Simplify *MORE THAN 1 VARIABLE (2x-‐3y)(-‐4x+2y+4) Ex #4 Expand and Simplify (4s-‐3t+3)(3t-‐5)-‐(3t-‐3)
Ex 5 Expand and Simplify (4s-‐3t+3)(3t-‐5)+2(3t-‐3)
3.8 Factoring Special Polynomials Two Types of Special Polynomials
1. Difference of Squares How to identify: ____________________________________________
____________________________________________
____________________________________________ How it works: Ex #1. 64m2-‐81 Ex #2. 16-‐49x2
Ex #3. 5x4-‐80y4
Ex #4. x2
25−y2
36
2. Perfect Square Trinomials How to identify: ____________________________________________
____________________________________________
____________________________________________ How it works:
Ex #5. x2-‐18x+81 Ex #6. 4x2+24x+36 Ex #7. 9x2-‐12x+4
Unit 3 Review Package
1. Which of the following powers is a perfect cube?
A. 32 B. 56 C. 64 D. 92
2. Determine a simplified expression for the lateral surface area of the prism below.
3. When 5x2 – 20 is factored, how many factors are in the result?
A. 2 B. 3 C. 4 D. 5
4.
5.
6.
7.
