UNIT 2 – FACTORING QUADRATIC EXPRESSIONS
Date Lesson Text TOPIC Homework
Feb.
21 2.0 Opt
Getting Started Pg. 74 # 2 - 13
Feb.
22
2.1
2.1
Working with Quadratic Expressions Pg. 85 # 2, 3, 5 – 7, 10, 11, 13,
14
Feb.
23
2.2
2.2
Factoring Polynomials:
Common Factoring
Pg. 93 # 2, 3, 5 – 8, 10, 12. 15
Feb.
24
2.3
2.3
Factoring Quadratic Expressions:
x2 + bx + c
Pg. 99 #2, 3, 5 – 9, 12 - 14
Feb.
27
2.4
Mid-Chapter Review Pg. 103 # 1, 3 – 5, 7, 9 - 11
Feb.
28
2.5
2.4
Factoring Quadratic Expressions:
ax2 + bx + c QUIZ ( 2.1 - 2.3)
Pg. 109 # 2, 4 – 10, 13
Mar. 1 2.6
2.5
Factoring Quadratic Expressions:
Special Cases
Pg. 115 # 2 - 12
Mar. 2 2.7
Review for Unit 2 Test Pg. 120 # 1, 3 – 6, 8, 9, 11 – 13
15 - 19
Mar. 3 2.8
(20)
UNIT 2 TEST
MCF 3M Lesson 2.0 Getting Started
Ex. 1. Match each word with the expression that best illustrates its definition.
Ex. 2. Simplify each expression
a) 222 10122687 xxyxxyxxy
b) )2()97()82( aababba
Ex. 3 Expand and simplify
)23(3)2(2 baba
Ex. 4 Common factor each expression completely.
a) 16124 2 xx
b) 542 963 xxx
Pg. 74 # 1 - 10
MCF 3M Lesson 2.1 Working with Quadratic Expressions
Ex. 1 Expand and simplify:
a) )7()42(3)3(2 xxx b) )3)(7( xx
c) 2572 yy d) yxyx 66
e) 232 x f) 221243 xx
Ex. 2 Evelyn is sewing a quilt as shown below. If the width of the border is x, determine a simplified expression
for the area of the quilt.
Pg. 85 # 2, 3, 5 – 7, 10, 11, 13, 14
MCF 3M Lesson 2.2 Common Factoring
Common factoring is the opposite of the
distributive property.
Ex. 1 Factor each of the following completely.
a) xx 3024 2 b) 243 352842 ppp
c) )1(4)1(3 xxx d) 233234 83612 yxyxyx
Ex. 2 A triangle has an area of xx 4812 2 and a height of 3x. What is the length of its base?
Ex. 3 Show that x3 is a common factor of )3(5)3(2 xxx .
Pg. 93 # 2, 3, 5 – 8, 10, 12. 15
MCF 3M Lesson 2.3 Factoring Quadratics in the form x2 + bx + c
ie: Find 2 integers that multiply to c and add to b.
Ex. Factor each of the following, completely.
a) 1272 xx b) 1892 xx
c) 22 103 yxyx d) 3242 xx
e) 12633 2 aa f) 48164 2 mm
Pg. 99 #2, 3, 5 – 9, 12 - 14
MCF 3M Lesson 2.4 Mid-Chapter Review
Pg. 103 # 1, 3 – 5, 7, 9 - 11
?
MCF 3M Lesson 2.5 Factoring Quadratics in the form ax2 + bx + c, a ≠ 1
When trying to factor a quadratic in the form ax2 + bx + c, a ≠ 1, the first thing you should do is determine if
there is a common factor.
Ex. 1 Factor completely.
2482 2 mm
If there is no common factor, we must factor the trinomial using other methods.
DECOMPOSITION - breaking a number or expression into parts that make it up
- Always check for a common factor
To factor using decomposition, we must find two integers that multiply to a x c, and add to b.
ie: For 3x2 – 11x – 4, Product = (3)(-4) = -12
Sum = -11
Factors = -12, 1
We then decompose the bx term into two terms using the integers found in step .
3x2 – 11x – 4
= 3x2 – 12x + x – 4
We then factor the four terms using a method called grouping. This involves grouping the four terms
into 2 groups of two terms and then common factoring each group
3x2 – 11x – 4
= 3x2 – 12x + x – 4
= [3x2 – 12x] + [x – 4]
= 3x[x – 4] + 1[x – 4] We should now have a common factor that we can factor out.
= (x – 4)( 3x + 1)
If the quadratic expression ax2 + bx + c, a ≠ 1 can be factored, then the factors are in the form
(px + r)( qx + s), where a = pq, c = rs, and b = ps + rq.
INSPECTION (a.k.a. – Guess and Check) Always check for a common factor
For 5x2 – 7x + 2, we want to find two terms that multiply to 5x
2 and 2 integers that multiply to 2.
ie: For 5x2 5x
and x (Never use negative integers for the x
2 term)
For 2 1 and 2 or -1 and -2 , since the middle term is negative, we should use -1 and -2
Try (5x -1)(x – 2) = 5x2
– 10x – x + 2 = 5x2
– 11x + 2 WRONG FACTORS !
Try (5x -2)(x – 1) = 5x2
– 5x – 2x + 2 = 5x2
– 7x + 2 CORRECT !
5x2 – 7x + 2 = (5x -2)(x – 1)
When you check your factors, do it to the side of the page or on a piece of scrap paper.
Ex. Factor completely.
a) 1572 2 xx b) 22 3108 yxyx (INSPECTION)
c) 31710 2 yy d) 22 4133 nmnm
e) 372 2 xx (INSPECTION) f) 3108 2 xx (INSPECTION)
Pg. 109 # 2, 4 – 10, 13
MCF 3M Lesson 2.6 Factoring Quadratics Expressions: Special Cases
Difference of Squares
Expand and simplify each of the following.
a) (x – 3)(x + 3) b) (2x – 1)(2x + 1) c) (3x + 2)(3x – 2)
What do you notice about each of the answers from the above examples?
Ex. 1 Factor each of the following completely.
a) x2 – 25 b) 4x
2 – 81
c) 25x4 – 49y
2 d) 224
25
4
9
1yxw
e) (x - y)2 – 4y
6 f) 256x
8 - 81
g) 22 )2( ba h) 22 )2()1( yx
Perfect Square Trinomials
Expand and simplify each of the following.
a) (x + 3)2 b) (2x – 1)
2 c) (3x – 2)
2
What do you notice about each of the answers from the above examples?
Ex. 1 Factor each of the following completely.
a) 4x2 + 12x + 9 b) 25x
4 – 40x
2 + 16
c) x2 – 12xy + 36y
2 d) 12x2 + 60x + 75
Perfect Square Trinomial can be factored using the methods learned previously, but it is quicker when you
recognize it as a perfect square trinomial. Pg. 115 # 2 - 12