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Algebra
Unit 6: Factoring
Name:
Date:
Period:
Factoring
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Page 629 #6 – 8; #15 – 20
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Page 629 #21, 22, 29- 32
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Worksheet
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Page 600 #19 – 42 Left
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Page 600 #21 – 43 Right **********Quiz Tomorrow**********
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Page 607 #5 – 8; #15 – 25 odd
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Page 607 #12 – 14; 20; 16 – 26 Even, and 27 – 39 LEFT
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Page 614 #5 – 8; #18 – 30 left
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Page 614 – 615 #15 – 17 ; #19 – 31 Middle; #33 – 46 left
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Page 614 – 615 #20 – 32 Right; #35 – 47 Right *****Quiz tomorrow****
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Page 622 #18 – 48 left
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Page 622 #20 – 50 right
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Page 629 #23 – 28, 33 – 36
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worksheet
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Page 608 #63, 64; page 630 #55 – 57; page 637 #44, 45
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worksheet
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Chapter review for test tomorrow
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Page 638 – 639 #9 - 17
10.8 GCF and Grouping (I,E/3) - Supplement
Factor by Greatest Common Factor (aka GCF) and Factor by Grouping
E1) Factor by GCF:
14x4 – 21x2
P1) Factor by GCF:
33x5 – 121x2
E2) Factor by Grouping: x3 + 2x2 +3x + 6
P2) Factor by Grouping: x3 + 4x2 + 6x + 24
E3) Factor Completely: 3m3 – 15m2 – 6m + 30
P3) Factor Completely: 2c4 + 2c3 – 24c – 24
*Note: If a polynomial can not be factored, then it is considered prime*
10.4 Solving Polynomial Equations in Factored Form (I, E/2)
Solving Polynomial Equations in factored form by applying the Zero Product Property (ZPP)
a
a=0
E1) Solve using the ZPP
3x(x + 7)(x – 3) = 0
E2) Solve using the ZPP
4(3x – 2)(x + 4) = 0
E3) Solve using the ZPP
(x – 2)(x + 3) = 0
E4) Solve using the ZPP
(x + 5)2 = 0
E5) Solve using the ZPP
(2x + 1)(3x – 2)(x – 1) = 0
•
OR
b
=0
b=0
P1) Solve using the ZPP
2y(y – 8)(y + 2) = 0
P2) Solve using the ZPP
7(2x + 3)(3x – 2) = 0
P3) Solve using the Zpp
( x – 4)(x + 1) = 0
P4) Solve using the ZPP
(x + 8)2 = 0
P5) Solve using the ZPP
(3x – 2)(4x + 3)(x + 4) = 0
10.5 Factor QT1 (x2 +bx +c) and Solve Quadratics by Factoring (I, E/2)
Factor Quadratic Trinomials with a leading coefficient of 1 (QT1)
There are many ways to factor trinomials (i.e. Guess and Check, ac method and the X method).
However, some polynomials cannot be factored. The Discriminant (b2 – 4ac) can be used to determine if
a trinomial can be factored. A quadratic trinomial can be factored (using integer coefficients) only if the
Discriminant is a perfect square.
*Note: If a polynomial can not be factored, then it is considered prime*
E1) Factor QT1: x2 + 3x + 2
P1) Factor QT1: x2 + 8x + 15
E2) Factor QT1: x2 – 5x + 6
P2) Factor QT1: x2 – 9x + 20
E3) Factor QT1: x2 – 2x – 8
P3) Factor QT1: x2 – 8x – 9
E4) Factor QT1: x2 + 7x – 18
P4) Factor QT1: x2 + 3x – 18
E5) Factor QT1: x2 + 3x – 6
P5) Factor QT1: x2 + 6x – 5
E6) Factor Completely: 4x3 + 20x2 + 24x
P6) Factor Completely: 5x3 – 25x2 – 30x
E7) Solve by Factoring (ZPP)
P7) Solve by Factoring (ZPP)
x2 – 3x = 10
x2 – 5x = 24
10.6 Factor QT2 (ax2 +bx +c) and Solve Quadratics by Factoring (I, E/3)
Factor Quadratic Trinomials with a leading coefficient that is not 1 (QT2)
There are many ways to factor trinomials (i.e. Guess and Check, ac method and the X method).
However, some polynomials cannot be factored. The Discriminant (b2 – 4ac) can be used to determine if
a trinomial can be factored. A quadratic trinomial can be factored (using integer coefficients) only if the
Discriminant is a perfect square.
*Note: If a polynomial can not be factored, then it is considered prime*
E1) Factor QT2: 2x2 + 11x + 5
P1) Factor QT2: 3 x2 + 5x + 2
E2) Factor QT2: 3x2 – 4x – 7
P2) Factor QT2: 2x2 + 21x – 11
E3) Factor QT2: 6x2 – 19x + 15
P3) Factor QT2: 8x2 – 14x – 15
E4) Factor Completely: 6x2 – 2x – 8
P4) Factor Completely: 6x2 + 9x – 27
E6) Solve by Factoring (ZPP)
P6) Solve by Factoring (ZPP)
21n2 + 14n + 7 = 6n + 11
8x2 + 10x – 11 = 12x + 10
10.7 Factor Special Products (DOTS and PST) and Solve Quadratics by Factoring (I, E/2)
Factoring Difference of Two Squares (DOTS) and Perfect Square Trinomials (PST)
Difference of Two Squares (DOTS)
a2 – b2
Original
(a + b)(a – b)
Perfect Square Trinomials (PST)
1.
a2 + 2ab + b2
(a + b)2
Factored Form
2.
a2 – 2ab + b2
(a – b)2
Original
Factored Form
Original
Factored Form
*Note: If a polynomial can not be factored, then it is considered prime*
E1) Factor DOTS:
a. m2 – 4
P1) Factor DOTS:
b. 4p2 – 25
E2) Factor PST:
a. x2 – 4x + 4
a. m2 – 9
b. 49q2 – 81
P2) Factor PST:
b. 16y2 + 24y + 9
a. x2 – 8x + 16
b. 9y2 + 60y + 100
E3) Factor Completely: 50 – 98x2
P3) Factor Completely: 12 – 27x2
E4) Factor Completely: 3x2 – 30x + 75
P4) Factor Completely: 2x2 – 12x + 18
E5) Solve by Factoring (ZPP)
P5) Solve by Factoring (ZPP)
-2x2 + 12x – 18 = 0
E6) Solve by Factoring (ZPP)
x2 + x + = 0
8x3 – 18x = 0
P6) Solve by Factoring (ZPP)
x2 - x + = 0
Factoring Application Problems (Area) (I,E/2)-Keystone Released
E1) You are putting a stone border along two sides of a rectangular Japanese garden that measures 6
yards by 15 yards. Your budget limits you to only enough stone to cover 46 square yards. How wide
should the border be?
x
15
garden
stone
6
x
E2) An object lifted with a rope or wire should not weigh more than the safe working load for the rope
or wire. The safe working load S (in pounds) for a natural fiber rope is a function of C, the circumference
of the rope in inches.
Safe working load model: 150 • C2 = S
You are setting up a block and tackle to lift a 1350 pound safe. What size natural fiber rope do you need
to have a safe working load?
E3) The width of a box is 1 inch less than the length. The height is 4 inches greater than the length. The
box has a volume of 12 cubic inches (V = l•w•h). What are the dimensions of the box?